question for temperature and heat

1. the ampification or gain of a transistor amplifier may depend on the temperature. The gain for a certain amplifier at room temperature (120.0○C) is 30.0, where as at 55○C it is 35.2. what would the gain be at 28○C if gain depend linearly on temperature over this limited range?
35.2 – 30.0 = 5.2
55.0 – 20.0 = 35.0○C
5.2 \ 35.0 = 0.15
28.0 -20.0 = 8.0
0.15 × 8.0 = 1.2
30.0 +1.2 = 3.2

2. A friend suffering from the flu has a fever; her body temperature is 38.6○C. What is her temperature in Kelvin?
Tk = 38.6 + 273.15 = 311.8 K

3. A cylinder contains 250L of xenon gas (Xc) at 20.0○C and pressure af 5.0 atm. How much heat is required to raise the temperature of this gas to 50.0○C, holding the volume constant? Threat the xenon aas an ideal gas.
P = 5.0 atm = 5.0 × (1.01×105 pa)
V = 250L = 250 × 10-3m3
T = 20.0○C + 273.15 = 293.15 ○K
N = PV/RT = (5.05×105pa) × (250×10-3m3)/(8.31J/mol.k)(393.15K) = 51.8 mol
∆T = 50.0 -20.0 = 30.0○C
Q = (3/2) n R∆T = (3/2)(51.8 mol)(8.31 J/ mol.C)(30.0○C) = 19kJ

4. A jewelry designer plans to make some specially ordere of silver charms for a commemorative braclet. If the melting point of silver is 960.8○C, how much heat must jeweler add to 0.500kg of silver at 20.0○C to be able to silver into her charm molds?
Q = mc∆T + mLf
Q= (0.500Kg)(0.235kJ/kg.C)(960.8○C-20.0○C) + (0.500Kg)(88.3kJ/kg)
= 110.5kJ + 44.15 kJ = 155kJ

5. A healthy person has an oral temperature of 98.6○F. what would this reading be an this Celsius scale.
F= 98.6○F - 32○F = 66.6○F
C=66.6○F(1/(9/5)) = 37.0○C

6. A block of concrete has a cross section of 8 m and a thickness of 10 cm. One side is at 40 C, and other is at 20 C. What is the rate of heat transfer?
Q/t = k . A [ (Thot – T cold) /d ]
= ( 1.7 Wm-1 K-1 ). (8m2). [(40○C – 20○C) /0.10 ]
= 2720W

7. Your whole family has taken showers before your, dropping the temperature in the water heater to 18○C. If the heater holds 150kg of water, how much energy will it take to bring it to 50○C?
∆Q = mc ∆T = (150Kg)(418.4J/kg.K)(50○C-18○C)
= 2.0 × 107 J

8. What temperature gradient must exist in a copper rod for it to transmit 33.5W/m2 of cross 10 ×10-5m down the rod?
Q/t = k. A [ (Thot – T cold) /d ]
33.5W/m2 = (385 Wm-1 K-1 ).( 10 ×10-5m) [ (Thot – T cold) /d ]
[ (Thot – T cold) /d ] = 33.5W/m2 ÷ (385 Wm-1 K-1 ).( 10 ×10-5m)
= 870○C/m

9. A steel beam is used in the roadbed of a brelge. The beam is mounted between two concrete support when the temperature is 23○C, with no room provided for thermal expansion. What compressional stress mush the concrete support apply to each end of the beam, if they are to keep the beam from expanding when the temparute rises to 42○C?
Stress= у∞∆T = (2.0×1011N/m2)(12×10-6(C)-1)(42○C-23○C) = 4.6 ×107N/m2

10. How much heat is required to raise the temperature of 0.20kg of water from 15○C to 45○C?
Q = mc∆T = (0.20kg)(4186J/kg.C)(45○C-30○C) = 2.5 × 104J