A diatomic gas (γ=1.4) does 200 J of work when it is expanded isobarically. The heat given to the gas in the process is:

The process described is an isobaric process, which means the pressure remains constant. In such a process, the work done by the gas is given by the formula:

W = PΔV

However, we don't have the values of pressure (P) and change in volume (ΔV). But we know that the work done is 200 J.

The heat given to the gas (Q) in an isobaric process can be calculated using the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W). This can be written as:

ΔU = Q - W

For a diatomic gas, the change in internal energy (ΔU) can be calculated using the formula:

ΔU = (f/2) nRT

where: f is the degrees of freedom of the gas, which is 5 for a diatomic gas, n is the number of moles, R is the gas constant, and T is the temperature.

However, we don't have the values of n and T. But we know that for an isobaric process, the heat Q can also be calculated using the formula:

Q = nCpΔT

where: Cp is the specific heat at constant pressure, which can be calculated using the formula Cp = γR / (γ - 1), where γ is the heat capacity ratio, which is 1.4 for a diatomic gas.

But again, we don't have the values of n and ΔT.

Given the information provided in the question, we cannot calculate the heat given to the gas without additional information.