An ideal gas is allowed to expand isothermally until it reaches its final volume

Question

An ideal gas is allowed to expand isothermally until it reaches its final volume. It is then heated at constant volume until it reaches its final pressure. The initial state of the gas is P1 -2.83 atm, V1 -1.00 L, and Eint 1 428 J, and its final state has volume V2 = 2.83 L and Eint 2-947 J. 1) Calculate the work done by the gas. Be careful with signs: if the work you calculate turns out to be, for example, -50 J in our sign convention, this means that 50 J of work were done by the gas. J Submit You currently have 0 submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question. 2) Find the heat absorbed by the gas during this process J Submit You currently have O submissions for this question. Only 5 submission are allowed. You can make 5 more submissions for this question.

Explanation / Answer

E1 = (f/2)n R T

E1 = (f/2)(PV)

putting values, f = 3

so E2 = (f/2)(P2 V2)

947 = (1.5)(P2)(2.83 x 10^-3)

P2 = 223086 Pa Or 2.20 atm

final process was isochoric process.

V ( at intermediate state) = V2 = 2.83 L

for isothermal.

P1 V1 = P V

P = (2.83 x 1) / (2.83) = 1 atm

1) Work done during isothermal process.

W = n R T ln(Vf /Vi) = P V ln(Vf/Vi)

W = (2.83 x 101325 x 10^-3) ln(2.83/1)

W = 298.3 J ....Work done by gas.

work done for constant volume process = 0

so net work done = - 298.3 J

2) for isothermal.

delta(U) = 0

so Q = W = 298.3 J

for isochoric process,

Work done = 0

so Q = deltaU = 946 - 428 = 519 J

heat absorbed = 298.3 + 519 = 817.3 J

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