1. Early in the morning, when the temperature is 5.0° C, gasoline is pumped into

Question

1. Early in the morning, when the temperature is 5.0° C, gasoline is pumped into a car's 49 L steel gas tank until it is filled to the top. Later in the day the temperature rises to 23° C. Since the volume of gasoline increases more for a given temperature increase than the volume of the steel tank, gasoline will spill out of the tank. How much gasoline spills out in this case? in Liters

2. A glass window 0.35 cm thick measures 61 cm by 36 cm. How much heat flows through this window per minute if the inside and outside temperatures differ by 17° C? in Kj

3. Assuming your skin temperature is 37.2° C and the temperature of your surroundings is 20.3° C, determine the length of time required for you to radiate away the energy gained by eating a 287 Calorie ice cream cone. Let the emmissivity of your skin be 0.915 and its area be 1.22 m2.? in hours

Explanation / Answer

You can use the volumetric expansion rate for both gas and steel.

.gas = 950 x 10^-6 /K

.steel = 36 x 10^-6 /K

Ref: Wiki: http://en.wikipedia.org/wiki/Coefficient...

Volumetric expansion of gas
V = V * T *
V = 49 * (18C) * 950 x 10^-6 /K
V = .8379

Volumetric expansion of steel tank
V = V * T *
V = 49 * (18C) * 36 x 10^-6 /K
V = .031752

Amount spilled = .8379 - .031752 = 0.806

2)  The steady-state heat flux (dq/dt = energy per unit time per unit area) across an infinite plate of a specified thickness (D) and thermal conductivity (K) whose two surfaces are kept at contant temperatures T1 and T2 is where T1 < T2

F = K*(T2-T1)/D, with the heat flow vector pointed in the direction of T1 (heat flows down the temperature gradient).

Ingnoring edge effects, the *total* heat transferred through an area A is then F*A.

Unfortunately, you are not given a value for K in this problem, so the best answer you can give is:

Heat flow = F*A = A*K*(T2-T1)/D

Heat flow = (0.61m * 0.36m)*K*(17 deg)/(3.5*10^-3 m)

Heat flow = (1066.628 m*deg)*K

Typical window glass has a thermal conductivity of ~1 W/(m*deg), (see first source) , so the heat flow through this pane of glass is about:

Heat flow = (1066.628 m*deg)*(1 W/(m*deg) = 1066.628 W

1 Watt = 1 J/sec, so in terms of kJ/min, 1 W = 6*10^-2 kJ/min, and the heat flow through the window would be:

1066.628 W * 0.06 (kJ/min)/W = 63.998 kJ/min

3) Skin temperature T = 37.2 + 273.15 = 310.35 K
Surrounding temperature To = 20.3 + 273.15 = 293.45 K
Emissivity e = 0.915
Stefan Boltzman constant sigma = 5.67 x 10-8 Watts m-2 K-4
Area A = 1.22 m^2
Energy E = 287 food calorie = 287 * 1000 cal = 287 * 1000 * 4.18 J = 1199660 J
Power P = e*sigma*A(T^4 - To^4)
= 0.915 * 5.67 x 10-8 * 1.22 * (310.35^4 - 293.45^4)
= 117.8257 W

Time t = E/P = 1199660/117.8257 sec = 10181.649 sec = 10181.649/3600 hour = 2.83 hour

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