Thermodynamics of Computer  Homework 2

ECSE 310 Thermodynamics of Computer, 
Homework 2

Each question has the same weight
P1) Using your own words, define the following:
1. Adiabatic process
2. Isothermal process
3. Thermal resistance
4. Emissivity
b) Answer the following:
1. What’s zeroth law of thermodynamics?
2. What’s the first law of thermodynamics? Write the formula and denote it carefully.
3. Explain thermal equilibrium and thermodynamic process.
4. Explain the difference between heat capacity, specific heat, and specific heat at constant
volume and pressure.
5. Explain the difference between fridge and heat pump.
6. Explain free expansion, constant-volume, and cyclical processes.
7. What’s an ideal gas?
8. When we measure temperature, we can determine?
A. Internal energy
B. Pressure.
C. rms speed.
D. A and C.
E. A, B and C.
9. Does the average translational kinetic energy of 3/2 kT applies to all ideal gas? (Yes/No)
P2) You are given a cup of hot tea (which is at 90 °C ) and a choice of either a stainless steel rod (thermal
conductivity 43 W/m∙°C) a wooden rod (thermal conductivity 0.17 W/ m∙°C) to stir it with. Assume
that both have a diameter of 5 mm and that when you hold them in your hand, 60 mm protrudes
from the hot liquid to where you hold it and that your fingers are at 33 °C.
a. What is the energy transfer rate along the rod in each case, neglecting any convection of heat
away from the rod?
b. Assuming that all heat is being absorbed in a skin volume of about 60 cubic mm, that the
specific heat of your skin is 3.47 J/g/°C and that the density of your skin is around that of
water (1 mg/mm3
), how quickly would your skin heat up by 5 °C in each case ? (Just a first
order estimate is fine – you don’t need to try to calculate the reduction in energy transfer
rate due to the increase in skin temperature; assume h =10 W/m2 K).
c. Assuming that the cup is very well insulated, except at the surface which has a diameter of
80 mm, what is the heat flux from the surface due to convection (assume still air above the
cup and a room temperature of 21 °C)?
d. What is the radiated heat flux from the surface of the cup (assume emissivity coefficient of
0.995 for water)? Blackbody radiation is given by 𝐽 = 𝜖𝜎𝑇
4
[
𝑊
𝑚2
] , where 𝜖 is the emissivity,
𝜎 is the Stefan-Boltzmann constant and 𝑇 is the temperature.
P3) A 300 mm2
silicon IC is 0.5 mm thick. It is attached to a silicone elastomer with a 75 μm thickness,
which is attached to a square heat sink of 650.25 mm2 area. The base of the heat sink is 2 mm thick,
and the length and thickness of the fins are 10 mm and 1.5 mm, respectively. The gap between the
fins is 1.5 mm (so there are 9 fins in total). The heat generation rate is 10 J/s. Assume temperature
at junction is 85°C.
a. Draw the equivalent thermal resistance network for these components, neglecting
convection for now. Calculate the thermal resistance of each element, assuming that
thermal conductivities are 130 W/m∙°C for silicon, 0.5 W/ m∙°C for elastomer and 202
W/m∙°C for the aluminum heat sink.
b. Now assume that the heat sink is cooled via convection, and that the model that we derived
in class for the average fin temperature holds here: 𝑇s≃
1
4
(3𝑇base+𝑇0) where Tbase is the
temperature at the base of the heatsink and T0 is the ambient air temperature. For an
ambient temperature of 21°C what heat transfer coefficient is required in order to maintain
the junction temperature of 85°C. Does this require forced air cooling (you need forced air
if h is larger than 50)?
P4) You are tasked with making a refrigerator by compressing and expanding an ideal gas. In the system,
the gas cycles between a volume of 0.5 L and 1 L. Assume that the gas is at atmospheric pressure
(100 kPa) in its compressed state, and that the room temperature is 21 °C and the internal
temperature of the fridge is 0 °C. Assume for now that all processes are reversible.
a. Complete the tables below, where the four points A,B,C and D correspond to the points of
the Carnot cycle given in class 
b. Now assume that you need to cool 250 mL of water from 21 °C to 0 °C by putting it inside
the fridge. (hint: mole number: 𝑛 =
𝑚
𝑣𝑚
. For water it is 18 g/mol)
1. How many cycles will it take?
2. By how much does the entropy of the water change on the first cycle?
3. By how much does the entropy of the water change in total?
4. If you find that the entropy has reduced, where has it gone?
5. Calculate the efficiency.