## 9 Common Problems of Heat

- Category: High School
- Written by fisikastudycenter

physics.fisikastudycenter.com - 9 common problems of heat, discussed at grade 10 of high school physics. Included heat,coefficients of thermal expansion, length expansion, area expansion and volume expansion, heat transfer.

**Problem 1**

A metal of 2500 g of mass takes 12 kJ of heat to raise its temperature. If the specific heat of this metal is 0,2 kalori/gr^{o}C and its initial temperature is 30^{o}C, find the final temperature of this metal!

**Answer**

Given :

Q = 12 kilojoule = 12000 joule

m = 2500 gram = 2,5 kg

T_{1} = 30^{o}C

c = 0,2 cal/gr^{o}C = 0,2 x 4200 joule/kg ^{o}C = 840 joule/kg ^{o}C

T_{2} =...?

Q = mcΔT

12000 = (2,5)(840)ΔT

ΔT = ^{12000}/_{2100} = 5,71 ^{o}C

T_{2} = T_{1} + ΔT = 30 + 5,71 = 35,71 ^{o}C

**Problem 2**

500 g of ice at −12^{o}C is heated to −2^{o}C. If the specific heat of ice is 0,5 cal/g^{o}C, find the amount of heat required for this process, express your answer in joule!

**Answer**

Data :

m = 500 gram

T_{1} = −12^{o}C

T_{2} = −2^{o}C

ΔT = T_{2} − T_{1} = −2^{o} − (−12 ) = 10^{o}C

c = 0,5 calorie/gr^{o}C

Q = ....?

Q = mcΔT

Q = (500)(0,5)(10) = 2500 calorie

1 calorie = 4,2 joule

Q = 2500 x 4,2 = 10500 joule

**Problem 3**

How much heat is required to change 500 g of ice at 0^{o}C to liquid water at 0^{o}C if the specific heat of ice is 0,5 cal/g^{o}C and the ice latent heat of fusion is 80 cal/g, show the answer in kilocalorie

**Answer**

Values given:

m = 500 gram

L = 80 calori/gr

Q = ....?

Q = mL

Q = (500)(80) = 40000 calori = 40 kcal

**Soal No. 4**

How much heat is required to change 500 g of ice at 0^{o}C to liquid water of 5^{o}C, if the specific heat of ice is 0,5 cal/g^{o}C, the specifc heat of water is 1 cal/g^{o}C and the ice heat of fusion is 80 cal/g!

**Answer**

The given values are:

m = 500 gram

c_{water} = 1 calori/gr^{o}C

L_{ice} = 80 calori/gr

Final temperature → 5^{o}C

Q = .....?

There are two steps in here

→ melting the ice , Q_{1} needed

Q_{1} = mL_{ice} = (500)(80) = 40000 calori

→ raising water temperature from 0^{o}C to 5^{o}C, Q_{2} needed

Q_{2} = mc_{water}_{r}ΔT_{water} = (500) (1)(5) = 2500 calori

Kalor total yang diperlukan:

Q = Q_{1} + Q_{2} = 40000 + 2500 = 42500 calori

**Problem 5**

Determine the the heat needed to change 500 g of ice at −10^{o}C to 5^{o}C of liquid water!

**Answer**

Data yang diperlukan:

m = 500 gram

c_{ice} = 0,5 calori/gr^{o}C

c_{water} = 1 cal/gr^{o}C

L_{ice} = 80 cal/gr

final temperature → 5^{o}C

Q = .....?

There are three steps in here:

→ raising ice temperature fromi −10^{o}C 0^{o}C, Q_{1} needed

Q_{1} = mc_{es}ΔT_{es} = (500)(0,5)(10) = 2500 calorie

→ melting ice , Q_{2} needed

Q_{2} = mL_{ice} = (500)(80) = 40000 calorie

→ raising water temperature from 0^{o}C to 5^{o}C, Q_{3} needed

Q_{3} = mc_{water}ΔT_{water} = (500)(1)(5) = 2500 kalori

So then

Q = Q_{1} +Q_{2} + Q_{3} = 2500 + 40000 + 2500 = 45000 calorie

** Problem 6**

What is the final temperature of a mixture contents 200 g of water at 80^{o}C and 300 g of water at 20^{o}C?

**Answer**

Given values

m_{1} = 200 gram

m_{2} = 300 gram

ΔT_{1} = 80 − t

ΔT_{2} = t − 20

final temperature = t = ......?

Q_{released} = Q_{taken}

m_{1}c_{1}ΔT_{1} = m_{2}c_{2}ΔT_{2}

(200)(1) (80 − t) = (300)(1)(t − 20)

(2)(1)(80 − t) = (3)(1)(t − 20)

160 − 2t = 3t − 60

5t = 220

t = 44^{o}C

**Problem 7**

You have a cup contents 200 g of water at 50°C. Your sister puts 100 g of ice at 0°C into the cup. Determine the final temperature of the water, assume that no heat is lost to the surroundings and no heat is taken by your cup!

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Use the specific heat heat of water 1 cal/gr°C, for ice 0,5 cal/gr°C, ice heat of fusion is 80 cal/gr.

**Answer**

The heat released by water (Q1) is the same in amount with the heat taken by ice to melt (Q2) and to raise temperature (Q3)

**Problem 8**

Given two bars of metals made from the same materials configured as below figure.

The lenght of P is doubles of the length of Q and the thermal conductivity of P is a half of Q. Determine the temperature of the juntion of the two bars!

**Answer**

Heat flow through two bars of same composition.

**Soal No. 9**

A steel tank with its coefficient of linear expansion 12 x 10^{-6}/°C, and its volume 0,05 m^{3 } is full of gasoline. The tank then is heated from 20°C. Find the volume of gasoline overflows from the tank when the temperature raise to 50°C, use the coefficient of volume expansion of gasoline 950 x 10^{-6}/°C !

**Answer**

The volume of gasoline that overflows

**prepared by: fisikastudycenter.com**