Week 2 and 3 – SS2 Second Term Physics Notes

 WEEKS TWO & THREE
HEAT CAPACITY AND SPECIFIC HEAT CAPACITY

• Heat capacity
• Specific heat capacity

MEASUREMENT OF HEAT ENERGY
In order to assess the quantity of heat energy possessed by a body, three quantities are needed. They are:

• the change in temperature (θ)
• the specific heat capacity of the body (C)
• mass of the body (m)

 The quantity of heat Q of a body is a product of the three quantities above as expressed by the equation.
                                        …1
It is measured in Joules

 Heat capacity
This is the quantity of heat required to raise the temperature of a substance by one degree. It is measured in Joules/K.

                                        …2

 Specific heat capacity
Specific heat capacity of a substance is the heat required to raise the temperature of a unit mass of the substance through one degree change in temperature
The quantity of heat Q received by a body is proportional to its mass (m), and temperature change and on the nature of the material the body is made of.
Thus;
                                        …3
                                    …4
C is a constant of proportionality called the specific heat capacity of the body, which depends on the nature of the body.
                                    …5
The unit of specific heat capacity is
It can be determined by using

• the method of mixtures
• the electrical method

 DETERMINATION OF SPECIFIC HEAT CAPACITY BY MIXTURE METHOD
The solid lead block is weighed on a balance to be M_s. A lagged calorimeter is dried and weighed to be M_c. It is then reweighed to be M_cw when half filled with water. The initial temperature of the water is taken to be θ₁.
The lead block is suspended in boiling water with a temperature θ₂ after which it is transferred to the calorimeter and the mixture stirred to maintain a uniform temperature θ₃
The specific heat capacity of the lead can be calculated using the fact that heat loss by the lead = heat gained by calorimeter and water.
Given the specific heat capacity of calorimeter and water to be C_s, C_c and C_w respectively
Heat loss by the lead = heat gained by calorimeter and water
            …6

                             …7

 
 DETERMINATION OF SPECIFIC HEAT CAPACITY BY ELECTRICAL METHOD
For a solid:
To calculate the specific heat capacity C_b of a solid brass block, we make two holes in a weighed brass block into which a thermometer and a heating element connected to a source of power supply are inserted. Oil is poured in the holes to ensure thermal conductivity. Assuming no heat is lost to the surrounding, the total amount of electrical heat energy supplied by the coil is equal to heat gained by the brass
Heat energy supplied by the coil = Heat gained by the brass
                                    …8

From ohms law,
                                        …9
So equation 8,                                    …10
                                    …11
For a liquid
                            …12

 
 
 
 
 
 CALCULATIONS ON SPECIFIC HEAT CAPACITY

• Calculations on specific heat capacity

Calculations on specific heat capacity

 EXAMPLE
250g of lead at 170⁰C is dropped into 100g of water at 0⁰C. If the final steady temperature is 12⁰C, calculate the specific heat capacity of lead. (C_w = 4.2 x 10³ Jkg^-1k^-1)

CLASSWORK 2 & 3

1. Define is heat capacity?
2. A metal of mass 0.5kg is heated to 100⁰C, transferred to a well lagged calorimeter of heat capacity 80 J/k containing water of heat capacity 420 J/k at 15⁰C. If the final steady temperature of the mixture is 25⁰C, find the specific heat capacity of the metal
3. Explain the meaning of the statement, the specific heat capacity of a substance is 777JKg^-1K^-1

 
 ASSIGNMENT 2 & 3
SECTION A

1. A waterfall is 630m high. What is the change in temperature of a quantity of water that falls from the top to the bottom of the waterfall? [Neglect heat lost to the surroundings, take acceleration due to gravity as 10ms^-2 and Specific capacity of water as 4200 JKg^-1K^-1] (a) 0.15⁰C (b) 1.50⁰C (c) 15.0⁰C (d) 21.0⁰C (e) 150.0⁰C
2. An electric heater rated 12V is used to heat 450g of water when a current of 5A was passed through it. What is the final temperature after 30minutes? [Specific capacity of water = 4200 JKg^-1K^-1] (a) 57k (b) 20k (c) 57k (d) 80k (e) 40k
3. If 60g of water at 90⁰C is poured into a calorimeter containing 20g of water at 30⁰C, calculate the final steady temperature of the mixture (a) 90⁰C (b) 75⁰C (c) 68⁰C (d) 25⁰C (e) 101⁰C
4. How much heat is required to change 10kg of an object from 20^OC to 70^OC? [Specific heat capacity of the object is 200JKg^-1K^-1](a) 1×10⁵J (b) 1×10⁴J (c) 40J (d) 10⁵J (e) 40×10⁵J
5. Which of the following is not used to determine the heat content of a body? (a) mass of the body (b) volume of the body (c) specific heat capacity of the body (d) temperature of the body (e) all of the above

SECTION B

1. A piece of copper of mass 120g is heated in an enclosure to a temperature of 125⁰C. It is then taken and held in the air for 30 seconds and dropped carefully into a copper calorimeter of mass 105g containing 200g of water at 20⁰C. The temperature of the water rises to 25⁰C. Calculate the rate at which heat is being lost from the copper when it is held in the air. [Specific heat capacity of copper = 400 JKg^-1K^-1, Specific capacity of water = 4200 JKg^-1K^-1]
2. An immersion heater supplies heat at the rate of 500Js^-1 (i) what is quantity of heat produced in 24 minutes (ii) if there is no heat loss, calculate the rise in temperature if a brass of 3kg initially at 30⁰C absorbed all the heat produced by the heater.