Q: A constant-volume gas thermometer is calibrated using the pressure and temperature scales shown in the first image. If the pressure at the lower fixed point (0°C) is $$9.09 \times 10^4$ Pa and at the upper fixed point (100°C) is 1.65$$ \times $$10^5 Pa$$, what Celsius temperature corresponds to a pressure reading of $$1.20 \times 10^5$ Pa?

$$T = \frac{1.20 \times 10^5$ - 9.09 \times 10^4$}{1.65 \times 10^5$ - 9.09 \times 10^4$} \times 100 = 47.5^\circ C$$

Q: A steel rod of length $$L_i = 2.0\ \mathrm{m} at$$ $$0^\circ \mathrm{C} is $$heated to $$50^\circ \mathrm{C}. If $$the coefficient of linear expansion for steel is $$\alpha = 11 \times 10$$^{-6}$$\ ^\circ \mathrm{C}^{-1}$$, what is the change in length $$\Delta L$$?

$$\Delta L = \alpha L_i \Delta T = 11 \times 10$$^{-6}$$ \times 2.0 \times 50 = 1.1 \times 10$$^{-3}$$\ \mathrm{m}$$

Q: If the original gap between two bolts (steel and brass) is $$5.0\ \mu\mathrm{m} at$$ $$27^\circ \mathrm{C}$$, the steel bolt is $$0.010\ \mathrm{m}$$, the brass bolt is $$0.030\ \mathrm{m}$$, and their coefficients of linear expansion are $$11 \times 10$$^{-6}$$/^\circ \mathrm{C}$$ and $$19 \times 10$$^{-6}$$/^\circ \mathrm{C}$$ respectively, at what temperature will the bolts touch?

$$\Delta T = \frac{5.0 \times 10$$^{-6}$$}{(0.010 \times 11 \times 10$$^{-6}$$) + (0.030 \times 19 \times 10$$^{-6}$$)} = 7.4^\circ \mathrm{C}$$;\ T = 27 + 7.4 = 34.4^\circ \mathrm{C}$

Q: A $$0.05\ \mathrm{kg}$$ ingot of metal is heated to $$200^\circ \mathrm{C}$$ and dropped into $$0.400\ \mathrm{kg} of $$water at $$20^\circ \mathrm{C}. $$The final equilibrium temperature is $$22.4^\circ \mathrm{C}. $$What is the specific heat capacity $$c_m of $$the metal? (Take $$c_w = 4186\ \mathrm{J/kg\cdot K})$$

$$c_m = \frac{0.4 \times 4186 \times (22.4 - 20.0)}{0.05 \times (200.0 - 22.4)} = 452.5\ \mathrm{J/kg\cdot K}$$

Question 1

A constant-volume gas thermometer is calibrated using the pressure and temperature scales shown in the first image. If the pressure at the lower fixed point (0°C) is $$9.09 	imes 10^4$ Pa and at the upper fixed point (100°C) is 1.65$$ 	imes $$10^5 Pa$$, what Celsius temperature corresponds to a pressure reading of $$1.20 	imes 10^5$ Pa?

Accepted Answer

$$T = \frac{1.20 	imes 10^5$ - 9.09 	imes 10^4$}{1.65 	imes 10^5$ - 9.09 	imes 10^4$} 	imes 100 = 47.5^\circ C$$

Question 2

Which of the following best explains why a metal tray feels colder than a plastic bottle when both are removed from the freezer, even though they are at the same temperature?

Accepted Answer

The metal tray has a higher thermal conductivity, so it transfers heat away from your hand more quickly.

Question 3

A steel rod of length $$L_i = 2.0\ \mathrm{m} at$$ $$0^\circ \mathrm{C} is $$heated to $$50^\circ \mathrm{C}. If $$the coefficient of linear expansion for steel is $$\alpha = 11 	imes 10$$^{-6}$$\ ^\circ \mathrm{C}^{-1}$$, what is the change in length $$\Delta L$$?

Accepted Answer

$$\Delta L = \alpha L_i \Delta T = 11 	imes 10$$^{-6}$$ 	imes 2.0 	imes 50 = 1.1 	imes 10$$^{-3}$$\ \mathrm{m}$$

Question 4

If the original gap between two bolts (steel and brass) is $$5.0\ \mu\mathrm{m} at$$ $$27^\circ \mathrm{C}$$, the steel bolt is $$0.010\ \mathrm{m}$$, the brass bolt is $$0.030\ \mathrm{m}$$, and their coefficients of linear expansion are $$11 	imes 10$$^{-6}$$/^\circ \mathrm{C}$$ and $$19 	imes 10$$^{-6}$$/^\circ \mathrm{C}$$ respectively, at what temperature will the bolts touch?

Accepted Answer

$$\Delta T = \frac{5.0 	imes 10$$^{-6}$$}{(0.010 	imes 11 	imes 10$$^{-6}$$) + (0.030 	imes 19 	imes 10$$^{-6}$$)} = 7.4^\circ \mathrm{C}$$;\ T = 27 + 7.4 = 34.4^\circ \mathrm{C}$

Question 5

Which equation correctly relates the Celsius and Kelvin temperature scales?

Accepted Answer

$$T_K = T_C + 273.15$$

Question 6

A $$0.05\ \mathrm{kg}$$ ingot of metal is heated to $$200^\circ \mathrm{C}$$ and dropped into $$0.400\ \mathrm{kg} of $$water at $$20^\circ \mathrm{C}. $$The final equilibrium temperature is $$22.4^\circ \mathrm{C}. $$What is the specific heat capacity $$c_m of $$the metal? (Take $$c_w = 4186\ \mathrm{J/kg\cdot K})$$

Accepted Answer

$$c_m = \frac{0.4 	imes 4186 	imes (22.4 - 20.0)}{0.05 	imes (200.0 - 22.4)} = 452.5\ \mathrm{J/kg\cdot K}$$

Question 7

Which of the following statements about the first law of thermodynamics is correct?

Accepted Answer

The change in internal energy of a system is equal to the heat added to the system minus the work done by the system: $$\Delta E_{int} = Q - W$$

Question 8

A monoatomic ideal gas undergoes an isothermal expansion from $$V_1 to$$ $$V_2 at $$temperature $$T. $$What is the work done by the gas?

Accepted Answer

$$W = nRT \ln \left( \frac{V_2$}{V_1$} \right)$$

Question 9

Which of the following processes results in no change in the internal energy of an ideal gas?

Accepted Answer

Isothermal process

Question 10

For a monoatomic ideal gas, what is the relationship between the molar specific heats at constant pressure ($$C_p) $$and constant volume ($$C_v$$)?

Accepted Answer

$$C_p - C_v = R$$

Question 11

A Carnot engine operates between a hot reservoir at $$T_h = 600\ \mathrm{K}$$ and a cold reservoir at $$T_c = 300\ \mathrm{K}. $$What is the maximum possible efficiency of this engine?

Accepted Answer

$$e = 1 - \frac{T_c}{T_h} = 1 - \frac{300}{600} = 0.5 or$$ $$50\%$$

Question 12

Which of the following is NOT an assumption of the kinetic theory of gases?

Accepted Answer

The forces between molecules are significant except during collisions.

Question 13

The average translational kinetic energy of a molecule in an ideal gas is given by which expression?

Accepted Answer

$$\frac{3}{2} k_B T$$

Question 14

A wall is made of two materials in series: material 1 with thickness $$L_1$$ and conductivity $$k_1$$, and material 2 with thickness $$L_2$$ and conductivity $$k_2. $$What is the correct expression for the steady-state rate of heat transfer $$P$$ through the wall?

Accepted Answer

$$P = \frac{A (T_h - T_c)}{\frac{L_1$}{k_1$} + \frac{L_2$}{k_2$}}$$

Question 15

According to the third law of thermodynamics, what happens to the entropy of a perfect crystal at absolute zero?

Accepted Answer

The entropy approaches zero.

Question 16

Which of the following statements about heat engines is correct?

Accepted Answer

No heat engine operating between two reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.

Heat and Thermodynamics: Structured Study Notes for PHY 103

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