Adiabatic Change in a Diatomic Gas

Adiabatic change is a thermodynamic process in which no heat is exchanged between the system and surroundings. In this case, pressure and temperature are related by the equation P@T^C, where C is a constant.

Finding the Value of C

To find the value of C, we can use the relationship between pressure, volume, and temperature for a diatomic gas given by the equation PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.

We can rearrange this equation to get P = (nR/V)T, which shows that pressure and temperature are directly proportional to each other for a fixed volume and number of moles.

For an adiabatic process, we know that PV^C is a constant, where C is the ratio of specific heats for a diatomic gas, given by C = Cp/Cv.

The value of C for a diatomic gas is 5/3, which means that P@T^5/3 is the relationship between pressure and temperature for an adiabatic change in a diatomic gas.

Therefore, the answer is option (1) 5/3.

Conclusion

In summary, an adiabatic change in a diatomic gas is characterized by the relationship between pressure and temperature given by the equation P@T^C. The value of C for a diatomic gas is 5/3, which means that pressure and temperature are related by the equation P@T^5/3.