Two containers, X and Y, both contain nitrogen gas at a temperature of 30 degree

Question

Two containers, X and Y, both contain nitrogen gas at a temperature of 30 degree C and a pressure of 1 atm. The initial volume of each of the containers is V_30 = 0.5 liters. The only difference between the two containers is that while container X has a piston that is sealed and cannot move, the gas in container Y is allowed to expand against the surrounding atmosphere. Q_X is the amount of heat required to raise the temperature of the gas in container X by 10 degree C, and Q_Y is the amount of heat required to raise the temperature of the gas in container Y by 10 degree C. What is the difference between Q_x and Q_Y? Use 0 degree C = 273.15 K Q_x - Q_y =

Explanation / Answer

P = 101325 Pa
V = 5*10^-4 m^3

Both containers have the same number of particles of identical gas, and the same change in temperature, So to raise the temperature by the same amount, we must add the same amount of internal energy to each X and Y.

QX = QV = U

QX - QY = U - (U + W) = -W
Where, Work done, W = p30 (V40 - V30)
Where, Work done, W = nRT = pV30 T / T30
W = (101325*5*10^-4*10)/(30 + 273.15)
W = -1.67 J

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