A large plane wall has a thickness L = 50 cm and thermal conductivity K = 25 W/m. K. On the left surface (x=0), it is subjected to a uniform heat flux q0 while the surface temperature To is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is TL = 225°C and the surrounding temperature is 25°C. The emissivity and the convection heat transfer coefficient on the right surface are 0.7 and 15 W/m^2, respectively. Required:
(a) Obtain the variation of temperature in the wall (T(x) in terms of qo, k, TL and L.
(b) Also, determine the value of heat flux (qo) and the temperature of the left surface of the wall ( at x=0).

An internally reversible refrigerator has a modified coefficient of performance accounting for realistic heat transfer processes of where qin is the refrigerator cooling rate, qout is the heat rejection rate, and is the power input. show that copm can be expressed in terms of the reservoir temperatures tc and th, the cold and hot thermal resistances rt, c and rt, h, and qin, as where rtot rt, c rt, h. also, show that the power input may be expressed as 1.39 a household refrigerator operates with cold- and hot-temperature reservoirs of tc 5 c and th 25 c, respectively. when new, the cold and hot side resistances are rc, n 0.05 k/w and rh, n 0.04 k/w, respectively. over time, dust accumulates on the refrigerator’s condenser coil, which is located behind the refrigerator, increasing the hot side resistance to rh, d 0.1 k/w. it is desired to have a refrigerator cooling rate of qin 750 w. using the results of problem 1.38, determine the modified coefficient of performance and the required power input w under (a) clean and (b) dusty coil conditions. internally reversible refrigerator qout qin w high-temperature reservoir low-temperature reservoir th th, i tc, i tc high-temperature side resistance low-temperature side resistance w qin th tc qinrtot tc qinrtot copm tc qinrtot th tc

A30 kg weight lies on top of a massless piston of area a = 0.01 m2 the exterior air is at a (constant) p =1 atm and t = 27 c. the interior gas is 0.4 moles of (ideal) n2 and it has initial temperature 27.00 degrees c. 1. what is the initial pressure in the interior? a. 29.4 kpa b. 130.7 kpa c. 101.3 kpa the next three questions concern what happens when an amount of heat q is slowly added to the interior, raising the piston by 1 mm and raising the interior temperature to 27.40 c

Given the position vector of the particle r(t)=(t+1)i+(t^2−1)j+2t k, find the particle's velocity and acceleration vectors at t=1