A sample of 8.02 × 10-1 moles of nitrogen gas (? = 1.40) occupies a volume of 2.

Question

A sample of 8.02 × 10-1 moles of nitrogen gas (? = 1.40) occupies a volume of 2.00 × 10-2 m3 at a pressure of 1.00 × 105 Pa and temperature of 300 K. The sample is adiabatically compressed to half its original volume. Nitrogen behaves as an ideal gas under these conditions.
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?
(iii) What is the amount of heat transferred from the gas to its environment?
(iv) Calculate the amount of work done in compressing the gas.

Explanation / Answer

Given change in volume dV = V-(V/2) = V/2 for isothermal compression change in temperature is zero (1) 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*10^5 pa )*(1.0*10^-2 m^3) = 10^3 j dS = 10^3 j/ 300 K = 3.330 (2) internal energy of the gas dU = nC_V dT =   0 (3) heat transffered dQ = (1.00*10^5 pa )*(1.0*10^-2 m^3) = 10^3 j (4) The amount work done on the system w = - pdV = - 1000 j t hope this will helps u In the problem after compression the gas must be expanded to return to the orizinal state

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