Question

A system does 1.80×10⁸ J of work while 7.50×10⁸ J of heat transfer occurs to the environment. What is the change in internal energy of the system, assuming no other changes (such as in temperature or by the addition of fuel)?

a) 5.70×10⁸ J
b) 6.30×10⁸ J
c) 7.20×10⁸ J
d) 8.10×10⁸ J

Answer 1

The change in internal energy of the system is found by applying the first law of thermodynamics. With the heat transfer to the environment being negative and the work done by the system being positive, the change in internal energy is -9.30×10⁸ J, expressed in magnitude as 9.30×10⁸ J

Step-by-step explanation:

To find the change in internal energy of the system, we must apply the first law of thermodynamics, which is expressed as ΔU = Q − W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In this case, the work done by the system is 1.80×10⁸ J and the heat transferred to the environment is 7.50×10⁸ J. Since the heat is transferred to the environment, it is negative in the context of the system gaining energy.

Therefore, the change in internal energy of the system (ΔU) can be calculated as follows:

• Q = −(7.50×10⁸ J) (negative because heat is leaving the system)
• W = 1.80×10⁸ J (positive because the system is doing work)
• ΔU = Q − W = −(7.50×10⁸ J) − (1.80×10⁸ J) = −(7.50 + 1.80)×10⁸ J = −(9.30×10⁸ J)

However, when expressing the answer, we typically drop the negative sign when asked for the magnitude of the change. Thus, the magnitude of the change in internal energy is 9.30×10⁸ J, which means the correct answer is not listed among the provided choices.