Physics: Heat and Thermodynamics Worksheet

Question 1

A 0.250 kg block of copper at 95.0°C is placed into 0.400 kg of water at 22.0°C in an insulated container. The specific heat of copper is 385 J/kg·°C and the specific heat of water is 4186 J/kg·°C. Assume no heat is lost to the container. Find the final equilibrium temperature.

Accepted Answer

The heat lost by the copper equals the heat gained by the water, so 0.250(385)(95.0 - T) = 0.400(4186)(T - 22.0). Solving gives T = 25.98°C, so the final equilibrium temperature is about 26.0°C.

Question 2

An ideal monatomic gas expands isothermally at 300 K from 2.00 L to 8.00 L. The gas contains 0.500 mol. Calculate the work done by the gas.

Accepted Answer

For an isothermal ideal gas expansion, W = nRT ln(Vf/Vi). Substituting gives W = (0.500)(8.314)(300) ln(8.00/2.00) = 1.73 × 10^3 J. The work done by the gas is about 1.73 kJ.

Question 3

A gas undergoes a process in which 750 J of heat is added to the gas and 420 J of work is done by the gas. Using the convention ΔU = Q - W, find the change in internal energy.

Accepted Answer

Using ΔU = Q - W, the change in internal energy is ΔU = 750 J - 420 J = 330 J. The internal energy of the gas increases by 330 J.

Question 4

A heat engine absorbs 2400 J of heat from a hot reservoir and rejects 1500 J of heat to a cold reservoir during each cycle. Find the work output and the thermal efficiency.

Accepted Answer

The work output is W = Qh - Qc = 2400 J - 1500 J = 900 J. The efficiency is e = W/Qh = 900/2400 = 0.375, so the engine is 37.5% efficient.

Question 5

A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. What is its maximum possible efficiency?

Accepted Answer

The Carnot efficiency is e = 1 - Tc/Th = 1 - 300/600 = 0.500. The maximum possible efficiency is 50.0%.

Question 6

A 2.00 mol sample of an ideal monatomic gas is heated at constant volume from 250 K to 400 K. Calculate the heat added. Use Cv = (3/2)R.

Accepted Answer

At constant volume, Q = nCvΔT. Using Cv = (3/2)R, Q = (2.00)(1.5)(8.314)(400 - 250) = 3.74 × 10^3 J. The heat added is about 3.74 kJ.

Question 7

A 1.50 mol sample of ideal diatomic gas expands adiabatically from 1.00 L to 3.00 L. Its initial temperature is 500 K. Use γ = 1.40. Find the final temperature.

Accepted Answer

For a reversible adiabatic process, TV^(γ - 1) is constant. Thus Tf = Ti(Vi/Vf)^(γ - 1) = 500(1.00/3.00)^0.40 = 322 K. The final temperature is about 322 K.

Question 8

A 0.600 kg sample of ice at 0°C is completely melted into water at 0°C. The latent heat of fusion of water is 3.34 × 10^5 J/kg. How much heat is required?

Accepted Answer

During melting at constant temperature, Q = mLf. Substituting gives Q = (0.600)(3.34 × 10^5) = 2.00 × 10^5 J. The required heat is about 200 kJ.

Question 9

A copper rod of length 0.750 m and cross-sectional area 1.20 × 10^-4 m^2 connects two thermal reservoirs at 100°C and 20°C. The thermal conductivity of copper is 400 W/m·K. Find the steady-state rate of heat conduction through the rod.

Accepted Answer

The conduction rate is P = kAΔT/L. Substituting gives P = (400)(1.20 × 10^-4)(80)/(0.750) = 5.12 W. Heat flows through the rod at a rate of 5.12 W.

Question 10

A blackbody radiator has a surface area of 0.0500 m^2 and temperature 800 K. Its surroundings are at 300 K. Use σ = 5.67 × 10^-8 W/m^2·K^4 and emissivity e = 1.00. Calculate the net radiated power.

Accepted Answer

The net radiated power is P = eσA(T^4 - Ts^4). Substituting gives P = (1.00)(5.67 × 10^-8)(0.0500)(800^4 - 300^4) = 1.14 × 10^3 W. The net power radiated is about 1.14 kW.

Question 11

One mole of an ideal gas expands freely into a vacuum from volume V to volume 4V in an insulated container. For an ideal gas, determine Q, W, ΔU, and ΔS.

Accepted Answer

For free expansion into a vacuum, W = 0 because there is no opposing pressure, and Q = 0 because the container is insulated. For an ideal gas, internal energy depends only on temperature, so ΔU = 0 and the temperature does not change. The entropy change is ΔS = nR ln(Vf/Vi) = R ln 4 = 11.5 J/K.

Question 12

A refrigerator removes 450 J of heat from its cold interior while 150 J of work is done on it during one cycle. Find the heat rejected to the room and the coefficient of performance.

Accepted Answer

Energy conservation gives Qh = Qc + W = 450 J + 150 J = 600 J. The coefficient of performance for a refrigerator is COP = Qc/W = 450/150 = 3.00.

Question 13

An ideal gas follows a rectangular cycle on a P-V diagram with corners at (V, P), (3V, P), (3V, 2P), and (V, 2P), traversed clockwise. Find the net work done by the gas in one cycle in terms of P and V.

Accepted Answer

The net work done by a clockwise cycle equals the area enclosed on the P-V diagram. The rectangle has width 3V - V = 2V and height 2P - P = P, so Wnet = 2PV. The gas does 2PV of work per cycle.

Question 14

A 3.00 mol sample of ideal gas is compressed isobarically at 2.50 × 10^5 Pa from 0.0400 m^3 to 0.0150 m^3. Find the work done by the gas and state whether energy is transferred into or out of the gas by work.

Accepted Answer

For an isobaric process, W = PΔV = (2.50 × 10^5)(0.0150 - 0.0400) = -6.25 × 10^3 J. The work done by the gas is negative, meaning 6.25 kJ of energy is transferred into the gas by work done on it.

Question 15

A 1.00 mol sample of an ideal gas is taken reversibly and isothermally at 350 K from volume V to volume 2V. Find the entropy change of the gas.

Accepted Answer

For a reversible isothermal expansion of an ideal gas, ΔS = nR ln(Vf/Vi). Substituting gives ΔS = (1.00)(8.314) ln 2 = 5.76 J/K. The entropy of the gas increases by 5.76 J/K.

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Physics: Heat and Thermodynamics

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