GRE Subject Test: Chemistry : Heat and Temperature

Study concepts, example questions & explanations for GRE Subject Test: Chemistry

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Example Questions

Example Question #1 : Heat And Temperature

Use the following values for water as needed.

\displaystyle \Delta H^o_{fus}=334\frac{J}{g}

\displaystyle \Delta H^o_{vap}=2260\frac{J}{g}

\displaystyle c=4.186\frac{J}{g^oC}

\displaystyle \rho = 1\frac{g}{mL}

If burning wood releases \displaystyle \small 20kJ of heat energy per gram of wood consumed, what mass of wood must be consumed to heat \displaystyle \small 1L of water from \displaystyle \small 20^oC to \displaystyle \small 100^oC, and then to convert it to water vapor?

Possible Answers:

\displaystyle 134g

\displaystyle 2595g

\displaystyle 17g

\displaystyle 335g

\displaystyle 130g

Correct answer:

\displaystyle 130g

Explanation:

There are two processes requiring added heat in this problem:

1. Raising the temperature of the liquid water from \displaystyle \small 20^oC to \displaystyle \small 100^oC (use \displaystyle \Delta Q = mc\Delta T)

2. Boiling the water at a constant temperature of \displaystyle \small 100^oC (use \displaystyle \Delta Q = m\Delta H^o_{vap})

To use either of these equation, we need to find the mass of the water using the relation between mass, density, and volume.

\displaystyle m = \rho*V= 1\frac{g}{mL}*1000mL=1000g

Use this mass with the given specific heat and temperatures to find the heat for part 1 of the process.

\displaystyle \Delta Q = (1000g)(4.186\frac{J}{g^oC})(100^oC - 20^oC)=334,880J

Then, use the mass with the given heat of vaporization to find the energy needed to convert the water to water vapor.

\displaystyle \Delta Q =(1000g) (2260\frac{J}{g})= 2,260,000J

Sum the energies for step 1 and step 2.

\displaystyle 334,880 J + 2,260,000 J = 2,594,880J\approx 2,595kJ

This is the total amount of energy needed from the burning wood. Use stoichiometry to find the grams of wood needed to produce this amount of energy.

\displaystyle 2595kJ*(\frac{1 g}{20kJ})=129.7g\approx 130g

Example Question #1 : Heat And Temperature

What was the final temperature of water if a \displaystyle 19 g sample of water absorbs \displaystyle 810.5 J of heat energy and heats up from \displaystyle 25^{o}C? (specific heat of water is \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 44^{o}C

\displaystyle 25^{o}C

\displaystyle 18^{o}C

\displaystyle 35^oC

Correct answer:

\displaystyle 35^oC

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle 810.5J=19g\times4.179\frac{J}{g^{o}C}\times(T_{f}-25^{o}C)

\displaystyle 810.5J=79.40\frac{J}{^{o}C}\times(T_{f}-25^{o}C)

\displaystyle \frac{810.5J}{79.40\frac{J}{^{o}C}}=T_{f}-25^{o}C

\displaystyle 10.21^{o}C=T_{f}-25^{o}C

\displaystyle T_{f}=35^{o}C

Example Question #1 : Heat And Temperature

An \displaystyle 81.9 g metal at \displaystyle 54.2^{o}C was put into \displaystyle 40.7g of water at \displaystyle 25^{o}C. The final temp of the water and metal was \displaystyle 29.3^{o}C. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C}.

Possible Answers:

\displaystyle 0.358\frac{J}{g^{o}C}

\displaystyle 4.8\frac{J}{g^{o}C}

\displaystyle 6.9\frac{J}{g^{o}C}

\displaystyle 2.4\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.358\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(81.9g\cdot C\cdot (29.3^{o}C-54.2^oC)=40.7g\cdot4.18\frac{J}{g^o}C(29.3^{o}C-25^{o}C)

\displaystyle -(-2039g^{o}C\cdot C)=731J

\displaystyle 2039g^{o}C\cdot\ C=731J

\displaystyle C=\frac{731J}{2039g^{o}C}=0.358\frac{J}{g^{o}C}

Example Question #1 : Heat And Temperature

Calculate the final temperature when a \displaystyle 44.0g sample of metal (specific heat of the metal=\displaystyle 0.52 \frac{J}{g^{o}C}) at \displaystyle 45.0^{o}C is placed into \displaystyle 95.0g of water at \displaystyle 23.0^{o}C. (specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C})

Possible Answers:

\displaystyle 132^{o}C

\displaystyle 76^{o}C

\displaystyle 17^{o}C

\displaystyle 24^{o}C

Correct answer:

\displaystyle 24^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(44.0g\cdot 0.52\frac{J}{g^{o}C}\cdot (T_{f}-45.0^oC)=95.0g\cdot4.18\frac{J}{g^o}C(T_{f}-23^{o}C)

\displaystyle -(22.9\frac{J}{^{o}C}(T_{f}-45.0^{o}C))=397\frac{J}{^{o}C}(T_{f}-23^{o}C)

\displaystyle -(22.9\frac{J}{^{o}C}\cdot T_{f}-22.9\frac{J}{^{o}C}\cdot 45.0^{o}C)=397\frac{J}{^{o}C}\cdot T_{f}-397\frac{J}{^{o}C}\cdot 23.0^{o}C

\displaystyle -(22.9\frac{J}{^{o}C}\cdot T_{f}-1031J)=397\frac{J}{^{o}C}\cdot T_{f}-9131J

\displaystyle -22.9\frac{J}{^{o}C}\cdot \ T_{f}+1031J=397\frac{J}{^{o}C}\cdot T_{f}-9131J

\displaystyle -22.9\frac{J}{^{o}C}\cdot \ T_{f}-397\frac{J}{^{o}C}\cdot T_{f}=-1031J-9131J

\displaystyle -419\frac{J}{^{o}C}\cdot T_{f}=-10162J

\displaystyle T_{f}=\frac{-10162^{o}C}{-419.9}=24^{o}C

 

Example Question #1 : Heat And Temperature

Calculate the specific heat of \displaystyle 19.3 g of metal that requires \displaystyle 353 J of heat energy to raise its temperature from \displaystyle 17.0^{o}C to \displaystyle 44.0^{o}C?

Possible Answers:

\displaystyle 0.677\frac{J}{g^{o}C}

\displaystyle 17\frac{J}{g^{o}C}

\displaystyle 0.581\frac{J}{g^{o}C}

\displaystyle 0.98\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.677\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

\displaystyle C=\frac{Q}{m\bigtriangleup T}=\frac{353J}{(19.3g\times (44.0^{o}C-17.0^{o}C))}=0.677\frac{J}{g^{o}C}

Example Question #31 : Thermodynamics And Phases

What was the final temperature of the water if a \displaystyle 33.0 g sample of water absorbs \displaystyle 423 J of heat energy and heats up from \displaystyle 23^{o}C? (specific heat of water is \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 71^{o}C

\displaystyle 54^{o}C

\displaystyle 28^{o}C

\displaystyle 117^{o}C

Correct answer:

\displaystyle 28^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Rearranging gives,

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle 423J=19g\times4.18\frac{J}{g^{o}C}\times(T_{f}-23^{o}C)

\displaystyle 423J=79\frac{J}{^{o}C}\times(T_{f}-23^{o}C)

\displaystyle \frac{423J}{79\frac{J}{^{o}C}}=T_{f}-23^{o}C

\displaystyle 5.35^{o}C=T_{f}-23^{o}C

\displaystyle T_{f}=28^{o}C

Example Question #41 : Physical Chemistry

A \displaystyle 20.5 g metal at \displaystyle 37.1^{o}C was placed in \displaystyle 23.3 g of water at \displaystyle 24.2^{o}C. The final temp of the water and metal was \displaystyle 26.0^{o}C. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C}.

Possible Answers:

\displaystyle 0.897\frac{J}{g^{o}C}

\displaystyle 2.32\frac{J}{g^{o}C}

\displaystyle 1.2\frac{J}{g^{o}C}

\displaystyle 0.77\frac{J}{g^{o}C}

Correct answer:

\displaystyle 0.77\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(20.5g\cdot C\cdot (26.0^{o}C-37.1^oC)=23.3g\cdot4.18\frac{J}{g^o}C(26.0^{o}C-24.2^{o}C)

\displaystyle -(-227.55g^{o}C\cdot C)=175.3092J

\displaystyle 227.55g^{o}C\cdot\ C=175.3092J

\displaystyle C=\frac{175.3092J}{227.55g^{o}C}=0.77\frac{J}{g^{o}C}

Example Question #361 : Gre Subject Test: Chemistry

What was the final temperature of the water if a \displaystyle 112 g sample of water absorbs \displaystyle 231 J of heat energy and heats up from \displaystyle 25.0^{o}C? (specific heat of water= \displaystyle 4.18\frac{J}{g^{o}C})

Possible Answers:

\displaystyle 134^{o}C

\displaystyle 25.5^{o}C

\displaystyle 43.2^{o}C

\displaystyle 75^{o}C

Correct answer:

\displaystyle 25.5^{o}C

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Rearranging gives,

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle 231J=112g\times4.18\frac{J}{g^{o}C}\times(T_{f}-25.0^{o}C)

\displaystyle 231J=468.16\frac{J}{^{o}C}\times(T_{f}-25.0^{o}C)

\displaystyle \frac{231J}{468.16\frac{J}{^{o}C}}=T_{f}-25.0^{o}C

\displaystyle 0.493^{o}C=T_{f}-25.0^{o}C

\displaystyle T_{f}=25.5^{o}C

Example Question #1 : Heat And Temperature

A \displaystyle 10.2 g metal at \displaystyle 72.9^{o}C was placed in \displaystyle 21.2 g of water at \displaystyle 25.0^{o}C. The final temp of the water and metal was \displaystyle 53.3^{o}C. Assuming heat was not lost to the surroundings find the specific heat of the metal? The specific heat of water is \displaystyle 4.18\frac{J}{g^{o}C}.

Possible Answers:

\displaystyle 465\frac{J}{g^{o}C}

\displaystyle 12.5\frac{J}{g^{o}C}

\displaystyle 2.6\frac{J}{g^{o}C}

\displaystyle 173\frac{J}{g^{o}C}

Correct answer:

\displaystyle 12.5\frac{J}{g^{o}C}

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

Heat is transferred from the metal to the water.

\displaystyle -Q_{metal}=Q_{water}

\displaystyle -(mC\bigtriangleup T)=mC\bigtriangleup T

\displaystyle -(mC(T_{f}-T_{i}))=-(mC(T_{f}-T_{i}))

\displaystyle -(10.2g\cdot C\cdot (53.3^{o}C-72.9^oC)=21.2g\cdot4.18\frac{J}{g^o}C(53.3^{o}C-25.0^{o}C)

\displaystyle -(-199.92g^{o}C\cdot C)=2507.83J

\displaystyle 199.92g^{o}C\cdot C=2507.83J

\displaystyle C=\frac{2507.83J}{199.92g^{o}C}=12.5\frac{J}{g^{o}C}

Example Question #361 : Gre Subject Test: Chemistry

How much heat is absorbed when \displaystyle 150 g of water goes from \displaystyle 25.0^{o}C to \displaystyle 35.0^{o}C? (Specific heat of water= \displaystyle 4.18 \frac{J}{g^{o}C})

Possible Answers:

\displaystyle 2270\ J

\displaystyle 70\ J

\displaystyle 6270\ J

\displaystyle 12\ J

Correct answer:

\displaystyle 6270\ J

Explanation:

Specific heat is the amount of heat needed to raise 1 gram of a substance by 1oC. Calorimeters used for these types of experiments because they are designed to be well-insulated, so no heat is gained from or lost to the surroundings. 

\displaystyle Specific\ heat(C)=\frac{amount\ of\ heat\ transferred(Q)}{(grams\ of\ substance,m)\times (temperature\ change\bigtriangleup, T)}

\displaystyle C=\frac{Q}{m\times \bigtriangleup T}

\displaystyle Q=mC\bigtriangleup T

\displaystyle Q=mC(T_{f}-T_{i})

\displaystyle Q=150g\cdot\ 4.18\frac{J}{g^{o}C}\cdot (35^{o}C-25^{o}C)

\displaystyle Q=6270\ J

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