Gas at a temperature of 100 C ° and a pressure of 10 ^ 5 Pa is isothermally compressed

| September 19, 2021 | education

Gas at a temperature of 100 C ° and a pressure of 10 ^ 5 Pa is isothermally compressed to a pressure of 1.5 * 10 ^ 5 Pa. To what temperature should this gas be cooled isochorically in order for the pressure to drop to its original value?

We give the values from given in the SI system:
t1 = 100 ° C = 373 K
1. In an isothermal process, the product of the pressure of a given mass of gas and its volume remains constant:
p1V1 = p2V2
2. In an isochoric process, the ratio of the pressure of a given mass of gas to its absolute temperature remains constant:
p2 / T2 = p3 / T3
In our case:
T2 = T1 (first process without temperature change)
p3 = p1 (by condition)
p2 / T1 = p1 / T3
Let us express T3 from this expression:
T3 = T1 * p1 / p2
Substitute the numerical values and calculate the temperature:
T3 = T1 * p1 / p2 = 373 * 10 ^ 5 / (1.5 * 10 ^ 5) = 248.6 K
Answer: it is necessary to cool the gas to a temperature of 248.6 K or -24 ° C.



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