Thermodynamics — Practice

Question 1

A gas absorbs 500 J of heat and does 200 J of work. Find the change in internal energy.

Accepted Answer

delta-U = Q - W = 500 - 200 = 300 J; the internal energy increases.

Question 2

Why can a heat engine never have 100% efficiency?

Accepted Answer

By the Kelvin-Planck statement of the second law, no process can have as its sole result the complete conversion of absorbed heat into work. Some heat must always be rejected to a cold reservoir, so Q2 can never be zero and efficiency is always below 100%.

Question 3

According to the law of equipartition of energy, what is the molar specific heat of a solid at ordinary temperature, and what is its approximate numeric value?

Accepted Answer

C = 3R (the Dulong-Petit law), approximately 3 x 8.314 = 24.9 J/mol/K. It matches experiment well at ordinary temperatures but breaks down at low temperature.

Question 4

2 moles of an ideal gas expand isothermally at 300 K from 5 L to 15 L. Find the work done (R = 8.314 J/mol/K).

Accepted Answer

W = mu R T ln(V2/V1) = 2 x 8.314 x 300 x ln(3) = 4988.4 x 1.0986 = 5480 J.

Question 5

A monatomic ideal gas is compressed adiabatically to 1/8 of its original volume. By what factor does its pressure increase?

Accepted Answer

gamma = 5/3 for a monatomic gas. P2/P1 = (V1/V2)^gamma = 8^(5/3) = (2^3)^(5/3) = 2^5 = 32. The pressure increases by a factor of 32.

Question 6

For a diatomic gas at ordinary temperature, Cv = 5R/2. Find Cp and gamma.

Accepted Answer

Cp = Cv + R = 5R/2 + R = 7R/2. gamma = Cp/Cv = (7R/2)/(5R/2) = 7/5 = 1.4.

Question 7

A Carnot engine operates between a source at 600 K and a sink at 300 K, absorbing 1000 J from the source per cycle. Find the efficiency and the heat rejected to the sink.

Accepted Answer

eta = 1 - T2/T1 = 1 - 300/600 = 0.5 = 50%. Q2 = Q1(1 - eta) = 1000 x 0.5 = 500 J rejected.

Question 8

In a cyclic process, a system absorbs 1000 J of heat and rejects 600 J. Find the net work done and the efficiency.

Accepted Answer

Since delta-U = 0 over a full cycle, W = Q1 - Q2 = 1000 - 600 = 400 J. eta = W/Q1 = 400/1000 = 40%.

Question 9

A Carnot engine absorbs 800 J from a reservoir at 400 K and rejects heat to a sink at 250 K. Find

Accepted Answer

A

Question 10

1 mole of a monatomic ideal gas at 300 K expands adiabatically until its volume doubles. Find the final temperature and the work done by the gas (R = 8.314 J/mol/K).

Accepted Answer

gamma = 5/3. T2 = T1 (V1/V2)^(gamma-1) = 300 x (0.5)^(2/3) = 300 x 0.630 = 189 K. W = mu R (T1 - T2)/(gamma - 1) = 8.314 x 111 / (2/3) = 1384 J.

Practice — Thermodynamics

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