Question

A gas enclosed in a cylinder by a piston that can move without friction is warmed, and 1000 J of heat enters the gas. Assuming that the volume of the gas is constant, the change in the internal energy of the gas is a) \(0 .\) b) 1000 J. c) -1000 J. d) none of the above.

Short answer

Answer: The change in internal energy of the gas is 1000 J.

Step-by-step solution

Determine the work done by the system

Since the volume of the gas is constant, there is no expansion or contraction of the gas, and consequently, the work done by the system (W) is zero.

Apply the first law of thermodynamics

Now we can apply the first law of thermodynamics, which is given by: ∆U = Q - W In this case, Q = 1000 J (heat added to the system) and W = 0 J (no work done by the system). Then, plug in the values to the equation: ∆U = 1000 J - 0 J

Calculate the change in internal energy

Now, we can calculate the change in internal energy of the gas: ∆U = 1000 J The change in internal energy of the gas is 1000 J, which corresponds to answer choice (b).