Question 397.
A gas is suddenly compressed to 10 times its original pressure . Calculate the rise in temperature of gas if its initial temperature is 27 degree C . take γ = 1.5.
Answer 397.
Sudden compression means there is hardly any time for heat exchange to occur with the environment which indicates that the process is adiabatic for which
PV^γ = constant
Also, for an ideal gas, PV = nRT => P^γ * V^γ = (nR)^γ * T^γ = constant * T^γ
taking ratio of these two eqns.,
P^(γ - 1) = (constant) * T^γ
=> (T2/T1)^γ = (P2/P1)^(γ - 1)
=> (T2/300)^(1.5) = (10)^(1.5 - 1)
=> T2 = (300) * (10)^(1/3)
=> T2 = 646 K
=> T2 = 373° C
=> rise in temperature of gas
= 373 - 27
= 346° C.
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A gas is suddenly compressed to 10 times its original pressure . Calculate the rise in temperature of gas if its initial temperature is 27 degree C . take γ = 1.5.
Answer 397.
Sudden compression means there is hardly any time for heat exchange to occur with the environment which indicates that the process is adiabatic for which
PV^γ = constant
Also, for an ideal gas, PV = nRT => P^γ * V^γ = (nR)^γ * T^γ = constant * T^γ
taking ratio of these two eqns.,
P^(γ - 1) = (constant) * T^γ
=> (T2/T1)^γ = (P2/P1)^(γ - 1)
=> (T2/300)^(1.5) = (10)^(1.5 - 1)
=> T2 = (300) * (10)^(1/3)
=> T2 = 646 K
=> T2 = 373° C
=> rise in temperature of gas
= 373 - 27
= 346° C.
Link to YA!
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