The first law of thermodynamics says that the variation of internal energy [tex]\Delta U[/tex] of a gas is equal to the amount of heat Q supplied to the gas minus the work W done by the gas:
[tex]\Delta U = Q-W[/tex]
The variation of internal energy of a gas is:
[tex]\Delta U = \frac{3}{2} n R \Delta T [/tex]
As it can be seen, it depends only on the variation of temperature [tex]\Delta T[/tex]. Since for an isothermal process [tex]\Delta T=0[/tex], then [tex]\Delta U=0[/tex]. This means that the first law of thermodynamics becomes
[tex]Q=W[/tex]
and since the work done is 370 J, then the amount of heat is also 370 J: [tex]Q=370 J[/tex].
