# Heat Temperature and Thermal Expansion Exam 2 and Problem Solutions

1. If Celsius thermometer shows the temperature of air 30⁰C, find the temperature of air in Fahrenheit thermometer. T(K)=T(C)+273

T=30+273=303⁰K

C/100=(F-32)/180

30/100=(F-32)/180

F=86⁰F

2. Find heat required to make 5g ice at -20⁰C to water at 30⁰C. (cice=0,5cal/g.⁰C, Lice=80cal/g, cwater=1cal/g.⁰C) Heat required to make ice at -20⁰C to ice at 0⁰C ;

Q₁=m.cice.ΔT=5.0,5.20

Q₁=50cal.

Heat required to make it melt;

Q₂=m.Lice=5.80

Q₂=400cal.

Heat to make it water at 30⁰C;

Q₃=m.cwater.ΔT=5.1.30

Q₃=150cal

Qtotal=Q₁+Q₂+Q₃=50+400+150=600cal

3. Two taps fill the water tank with different flow rates. Tap A fills the tank in 1 hour and tap B fills the tank in 3 hour If we open two taps together, find the final temperature of the water in the tank. Flow rates of taps;

VA=3VB

3m.c.(T-10)=m.c(50-T)

T=20⁰C

4. When we decrease the temperatures of the rods ΔT, relation between the final lengths of rods becomes; L₁<L₂<L₃. Find the relation between αA, αB and αC. Since change in length of the rod 1 is larger than the rod 2;

αA<αB

Since change in length of the rod 2 is larger than the rod 3;

αC<αA

αC<αA<αB

5. Length vs. temperature graph of A, B and C is given below. Find the relation between λA, λB and λC. Slope of the graph=ΔL/ΔT=L₀.λ

Initial length of A is larger than C but slopes of them are equal, so;

λC>λA

B and C have same length but slopes of them are different.

λB >λC

λB >λC>λA