Please show all work, thank you.

Problem 1: A closed, adiabatic, 1000m room contains 60 students. Perform energy balances on the room and the students, assuming each behaves as an ideal gas and has constant mass. Assume heat transfer between the room and the students is governed by Newton's law of cooling and that the body generates heat at a constant rate of 80W. b. Evaluate the differential equations using a Laplace transform to express the temperature of the room and the students as a function of time. Mbody = 70kg J Cy.body = 3.470- = 8.K = 80W U body W = 4.5 mK = 1.8m? | Abody Pair = 1.225 kg m J |Cy air g.K V = 1000m = = 0.72 room 298.15K "room (o). Loa (0) = 310K