(c) A sample of 8.02 x 10 moles of nitrogen gas (withy 1.40) occupies a volume o

Question

(c) A sample of 8.02 x 10 moles of nitrogen gas (withy 1.40) occupies a volume of 2.00 x 10-2m3 at a pressure of 1.00 x 105 Pa and temperature of 300K. The sample is adiabatically compressed to exactly half its original volume. Nitrogen behaves as an ideal gas under these conditions. (i) What is the change in entropy of the gas? lition 6 marks) constant, and hence determine the final temperature of the gas. (d) The gas sample is now returned to its initial state and then isothermally compressed to half its original volume (i) Find the change in entropy of the gas. ii) What is the change in internal energy of the gas? ii What is the amount of heat transferred from the gas to its environment? iv) Calculate the amount of work done in compressing the gas. 8 marks)

Explanation / Answer

Part C)

i) Change in entropy, dS = dQ/T

where dQ = dU+P*dV = P*dV.

so dS = 1*105*1*10-2/300

Change in Entropy, dS = 3.333

Part(d)

Given change in volume dV = V - (V/2) = V/2

for isothermal compression change in temperature is zero

(i)The change in entropy dS = dQ / T

according to first law of thermodynamics

dQ = dU + p*dV

for isothermal process dU = 0

dQ = pdV = (1.00*105 pa )*(1.0*10-2 m3) = 103 J

dS = 103 J/ 300 K = 3.330

(ii) internal energy of the gas, dU = nCvdT = 0

(iii) heat transffered dQ = (1.00*105 Pa )*(1.0*10-2 m3) = 103 J

(iv) The amount work done on the system w = - pdV = - 1000 J

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