# 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**