Question

for ideal gas the PVT equations are given by P1(V1) ^k =P2(V2) ^k and P1V1/T1 = P2V2/T2. where P, V, T are pressure, volume, temperature respectively and k is a constant show that T1/T2=(V2/V1) ^k-1​

Answer 1

Explanation:

We know that

`P_1V_1^k = P_2V_2^k`

or

`\left((P_1)/(P_2) \right) = \left((V_2)/(V_1) \right)^k` (1)

and

`(P_1V_1)/(T_1) = (P_2V_2)/(T_2)` (2)

Let's move the P and V variables in Eqn(2) to the right side:

`(T_1)/(T_2) = \left((P_1)/(P_2) \right)\left((V_1)/(V_2) \right)` (3)

Substitute Eqn(1) into Eqn(3):

`(T_1)/(T_2) = \left((V_2)/(V_1) \right)^k \left((V_1)/(V_2) \right)`

`\:\:\:\:\:\:\:= \left((V_2)/(V_1) \right)^(k-1)`