Question 1

Which statement best describes the First Law of Thermodynamics?

Accepted Answer

Energy in the universe is conserved and can be transferred as heat or work: $$\Delta U = q + w.$$

Question 2

A gas in a piston undergoes an isochoric process. Which of the following is true?

Accepted Answer

No work is performed: $$w = 0$$, so $$q = \Delta U.$$

Question 3

For a monatomic ideal gas, what is the value of the molar heat capacity at constant volume $$C_V$$?

Accepted Answer

$$C_V = \frac{3}{2}R$$

Question 4

Which of the following is a correct mathematical statement about state functions?

Accepted Answer

State functions have exact differentials if $$\frac{\$$partial^2$$ z}{\partial x \partial y} = \frac{\$$partial^2$$ z}{\partial y \partial x}.$$

Question 5

During an isobaric process, which equation correctly relates heat transfer to temperature change?

Accepted Answer

$$q_p = nC_p \Delta T$$

Question 6

Which of the following is NOT a form of work commonly considered in thermodynamics?

Accepted Answer

Heat transfer

Question 7

If a process is reversible, how does the work done compare to an irreversible process for the same change in state?

Accepted Answer

Reversible work is always greater than irreversible work.

Question 8

For a diatomic ideal gas, what is the value of $$C_p$$?

Accepted Answer

$$C_p = \frac{7}{2}R$$

Question 9

Which equation correctly defines enthalpy $$H in $$terms of internal energy $$U$$, pressure $$P$$, and volume $$V$$?

Accepted Answer

$$H = U + PV$$

Question 10

A sample of gas undergoes a constant volume process. If $$n = 2$$ mol, $$C_V = 12.5 J/$$mol·K, and $$\Delta T = 10 K$$, what is the change in internal energy $$\Delta U$$?

Accepted Answer

$$\Delta U = 250 J$$

Question 11

Which of the following is a path function?

Accepted Answer

Work $$w$$

Question 12

In a laboratory experiment, a gas expands against a constant external pressure. Which formula should be used to calculate the work done by the gas?

Accepted Answer

$$w = -P_{ext} \Delta V$$

Question 13

Which relationship between $$C_p$$ and $$C_V is $$correct for an ideal gas?

Accepted Answer

$$C_p = C_V + R$$

Question 14

A process occurs at constant pressure. Which equation gives the heat transferred to the system?

Accepted Answer

$$q_p = \Delta H$$

Question 15

Which of the following is true about the change in a state function?

Accepted Answer

It is independent of the path taken and depends only on the initial and final states.

Question 16

A gas undergoes an adiabatic expansion. Which of the following is true?

Accepted Answer

No heat is transferred: $$q = 0.$$

Question 17

Which equation is used to check if a differential $$dz is $$exact?

Accepted Answer

$$\frac{\$$partial^2$$ z}{\partial x \partial y} = \frac{\$$partial^2$$ z}{\partial y \partial x}$$

Question 18

Which process is characterized by constant temperature?

Accepted Answer

Isothermal

Question 19

For a liquid or solid, which equation gives the relationship between $$C_p$$ and $$C_V$$?

Accepted Answer

$$C_p = C_V$$

Question 20

A sample of diatomic ideal gas ($$n = 1$$ mol) is heated at constant pressure from $$T_1 = 300$ K to T_2$ = 400 K. $$What is the heat absorbed $$q_p$$? (Use $$C_p = \frac{7}{2}R$$, $$R = 8.314 J/$$mol·K)

Accepted Answer

$$q_p = 2910 J$$

The First Law of Thermodynamics: Energy, Heat, and Work

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