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Chapter 12: Problem 27

A gas expands under constant pressure \(P\) from volume \(V_{1}\) to \(V_{2}\). The work done by the gas is (A) \(P\left(V_{2}-V_{1}\right)\) (B) \(P\left(V_{1}-V_{2}\right)\) (C) \(P\left(V_{1}^{\gamma}-V_{2}^{\gamma}\right)\) (D) \(\frac{P V_{1} V_{2}}{V_{2}-V_{1}}\)

Short Answer

Expert verified
The correct answer is \(A) P(V_2 - V_1)\), which matches the formula for work done under constant pressure: \(W = P * (V_2 - V_1)\).

Step by step solution

01

Identify the formula for work done under constant pressure

To find the work done by the gas, we need to use the formula for work done under constant pressure, which is given by W = P * (V2 - V1), where W is the work done, P is the constant pressure, V1 is the initial volume, and V2 is the final volume.
02

Compare the formula to the provided answer choices

Now, let's look at each answer choice to see which one matches the formula from step 1. (A) \(P(V_2 - V_1)\): This matches the formula for work done under constant pressure. (B) \(P\left( V_1 - V_2 \right)\): This is incorrect because the formula for work done under constant pressure involves the subtraction of the initial volume V1 from the final volume V2, not vice versa. (C) \(P\left( V_1^{\gamma} - V_2^{\gamma} \right)\): This is incorrect because the formula for work done under constant pressure does not involve raising the volumes to any power, gamma. (D) \(\frac{P V_1 V_2}{V_2 - V_1}\): This is incorrect because the work done under constant pressure should be the product of the pressure P and the difference in volumes, V2 - V1.
03

Select the correct answer

Since answer choice (A) is the only one that matches the formula for work done under constant pressure, we can conclude that the correct answer is \(A) P(V_2 - V_1)\).

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Most popular questions from this chapter

A vertical cylinder with a massless piston is filled with one mole of an ideal gas. The piston can move freely without friction. The piston is slowly raised so that the gas expands isothermally at temperature \(300 \mathrm{~K}\). The amount of work done in increasing the volume two times is \(R=\frac{25}{3} \mathrm{~J} / \mathrm{mol} / \mathrm{K}, \log _{\mathrm{e}} 2=0.7\) (A) \(1750 \mathrm{~J}\) (B) \(2500 \mathrm{~J}\) (C) \(750 \mathrm{~J}\) (D) \(4250 \mathrm{~J}\)

Which one of the following statements is incorrect? (A) If positive work is done by a system in a thermodynamic process, its volume must increase. (B) If heat is added to a system, its temperature must increase. (C) A body at \(20^{\circ} \mathrm{C}\) radiates in a room, where room temperature is \(30^{\circ} \mathrm{C}\). (D) If pressure vs temperature graph of an ideal gas is a straight line, then work done by the gas is zero.

For an adiabatic expansion process, the quantity \(P V\) (A) decreases. (B) increases. (C) remains constant. (D) depends on adiabatic exponent of the gas.

In the arrangement shown in Fig. \(12.17\), gas is thermally insulated. An ideal gas is filled in the cylinder having pressure \(P\) greater than atmospheric pressure \(P_{0}\). The spring of force constant \(K\) is initially upstretched. The piston of mass \(m\) and area s is frictionless. In equilibrium, the piston rises up a distance \(x_{0}\), then (A) Final pressure of the gas is \(P_{0}+\frac{K x_{0}}{s}+\frac{m g}{s}\). (B) Work done by the gas is \(\frac{1}{2} K x_{0}^{2}+m g x_{0}\). (C) Decrease in internal energy of the gas is \(\frac{1}{2} K x_{0}^{2}+m g x_{0}+P_{0} s x_{0}\) (D) All of the above.

Two gases have same initial pressure, volume, and temperature. They expand to same final volume, one adiabatically and the other isothermally. (A) The final temperature is greater for isothermal process. (B) The final temperature is lesser for isothermal process. (C) The work done by the gas is greater for isothermal process. (D) The work done by the gas is greater for adiabatic process.
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