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PV nRT Phys 265 wc3D Name: 6. Iced tea is made by adding ice to 3.8 kg of hot te

ID: 1732126 • Letter: P

Question

PV nRT Phys 265 wc3D Name: 6. Iced tea is made by adding ice to 3.8 kg of hot tea, initially at 80°C. How many kg of ice, initially at 0°C, are required to bring the mixture to 10°C? (L 3.33 x 105 Jlkg, Cw 4,186 J/kg°C) 7. An object at 17°C has its temperature increased to 47°C. The power then radiated by this object increases by how many percent? 8. A system is acted on by its surroundings in such a way that it receives 22 J of heat while simultaneously doing 62 J of work. What is its net change in internal energy? The volume of an ideal gas changes from 0.30 m3 to 0.55 m3 although its pressure remains constant at 20,000 Pa. What work is done on the system by its environment? 9. 10.A heat engine operating between a pair of hot and cold reservoirs with respective temperatures of 500 K and 200 K will have what maximum efficiency? p. 2

Explanation / Answer

(1) We know that ideal gas follow the
PV = nRT --------(1)
where P is pressure
V is volume
n is no. of moles
R is characterstics of gas constant
T is temperature in Kelvin
If we increase the temperature by factor 5 , i.e.
T2 = 5T
Hence
PV2 = nRT2 --------(2)
Now taking ratio of 2 and 1
(V2/V) = (T2/T)
V2/V = (5T/T) = 5
V2 = 5V
hence the volume will increase by factor of 5 .
(2) Pressure of gas = 25 atm
volume = 4 L
no. of moles (n) = (1/2)
R = 0.0821 Latm/mol-K
T is temperature in Kelvin
Now using the ideal gas equation
PV = nRT
25*4 = (1/2)*0.0821*T
T = 2436.054 K
(3) Molecular mass of nitrogen = 28 gram
That means
1 mole = 28 gram
5 moles = 5*28 = 140 gram
Therefore the 140 gram gas will present in the cylinder.

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