Question

N moles of an ideal gas undergo a process in which the temperature changes with volume as T=KV². The work done by the gas as the temperature changes from T0 to 4T₀ is:

A. 3nRT₀
B. (5/2)nRT₀
C. (3/2)nRT₀
D. Zero

Answer 1

The work done by the gas as the temperature changes from T₀ to 4T₀ is zero. The correct option is D.

Step-by-step explanation:

The work done by the gas can be calculated using the formula:

W = ∫PdV

Since the gas is undergoing a process in which the temperature changes with volume as T = KV², we can substitute this equation into the equation for work:

W = ∫PdV = ∫nRT/V dV = nRT ∫(1/V) dV

Integrating from the initial volume V₀ to the final volume V, we get:

W = nRT ln(V/V₀)

The work done by the gas as the temperature changes from T₀ to 4T₀ is:

W = nRT₀ ln(4T₀/T₀)

W = nRT₀ ln(4)

So, the correct option is D. Zero, since the natural logarithm of 4 is not zero.