Question

Three moles of an ideal gas are compressed isothermally and reversibly to a volume of 2L. The work done is
2983 id at 22°C. Calculate the initial volume of the gas. 3
2.8 x 10 kg of nitrogen is expanded isothermally and reversibly at 300 K from 15.15 x 109 Nm when the
19293 moles of an ideal gas are compressed isothermally and reversibly to the volume of 2 litre the work done is 2.98 3 kilo joule at 20 degree Celsius calculate the initial volume of the gas ​

Answer 1

This has two questions it seems. First question is understandable ,but the second has no proper information to solve.

First question is solved below.

The initial volume of the gas is : 3 L

• Given, number of moles of gas = 3, Final volume of gas = 2L
• Also it is given as isothermal and reversible compression
• Work done = 2.983 KJ, Temperature = 22°C = 273+22 = 295 K
• Now, we know for isothermal reverrsible expansion or compression Work done is given by,
• W = -2.303nRT log(V2/V1) , where n is number of moles, R is rydberg constant, T is temperature , V2 and V1 are final and initial volume respectively.
• Now,  using data:                                                                                     2.983 * 10^3  = - 2.303 * 3 * 8.314 * 295 * log( 2/V1)
• 2.983 * 10^3 = -16945.22 log (2/V1)
• -0.176 = log (2/V1)
• -0.176 = log 2 - log V1  = -0.176 = 0.3010 - log V1
• log V1 = 0.4777     ;  V1 = antilog 0.477 =  3
• So V1 = 3L

Answer 2

Hey there , your answer is here. I hope it'll be helpful