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Determination Of Specific Heat Capacity Of A Given Solid - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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2 Questions around this concept.

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An experiment is conducted to determine the specific heat capacity (c) of a metal using the method of mixtures. A known mass of the metal at a temperature T¹ = 100°C is placed in a calorimeter containing a known mass of water at a lower temperature T₂ = 20°C. The final equilibrium temperature T_f is observed to be 30°C. Given that the mass of the metal is m₁ = 0.2 kg and the mass of water is m₂ = 0.5 kg, calculate the specific heat capacity of the metal.

150 J/kg°C

2500 J/kg°C

1100 J/kg°C

1500 J/kg°C

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Concepts Covered - 1

Determination of specific heat capacity of a given solid

Aim:
To determine specific heat capacity of a given solid by method of mixtures.

Apparatus:
A hypsometer, calorimeter, stirrer, a lid and outer jacket, given solid in powder form or in small pieces,
balance, weight box, two half degree thermometer, cold water, clamp stand.

Theory:
In hypsometer, the solid is heated uniformly above room temperature up to a fixed temperature and then
solid is added to cold water in calorimeter.
Heat lost by solid = Heat gained by the water and calorimeter.

Procedure:
1. Put two thermometer A and B in a beaker containing water and note their reading. Take one of them,
say A to be standard and find the correction to be applied to the other, say B.
2. Put thermometer B in copper tube of hypsometer containing the powder of given solid. Put sufficient
water in hypsometer and place it on a burner.
3. Weigh the calorimeter with stirrer and lid over it by the physical balance. Record it.

4. Fill about half of calorimeter with water at about temperature 5⁰C to 8⁰C below room temperature. Now,
weigh it again and record it.
5. Heat the hypsometer about 10 minutes till the temperature of solid remains steady.
6. Note the temperature of water in the calorimeter. Now, transfer the solid from hypsometer to the
calorimeter quickly. Stir the contents and record the final temperature of the mixture.
7. Remove the thermometer A from calorimeter and weigh the calorimeter with its contents and lid.

Observations:

1. $\text { Reading of thermometer A} {=T_{A}=\ldots \ldots _{}^{0}\textrm{C}$

2. $\text { Reading of thermometer B} {=T_{B}=\ldots \ldots _{}^{0}\textrm{C}$

3. $\text{Correction applied in w.r.t A}= {\left(T_{A}-T_{B}\right)=\ldots . . . _{}^{0}\textrm{C}$

4. $\text { Mass of calorimeter and stirrer } {m=\ldots \ldots \mathrm{g}}$

5. $\text { Water equivalent of calorimeter }= {w=m \times 0.095=\ldots \ldots \mathrm{g}}$

6. $\text { Specific heat of copper calorimeter } {=0.095 \mathrm{cal} /\mathrm{g}}$

7. $Mass \ of \ calorimeter \ +\ stirrer + lid \quad=m_{1}=\ldots \ldots \mathbf{g}$
8. $Mass\ of \ calorimeter + stirrer + lid + cold\ water =m_{2}=\ldots \ldots \mathbf{g}$
9. $Steady \ temperature\ of\ hot\ solid \quad=T_{S}=\ldots . .^oC$
10. $Corrected\ temperature\ of\ hot\ solid\ T=T_{S}-\left(T_{A}-T_{B}\right)=\ldots . .^{\circ} \mathrm{C}$
11. $Temperature \ of \ cold\ water \quad=t=\ldots . .^{\circ} \mathrm{C}$
12. $Temperature\ of\ mixture \quad=\theta=\ldots . .^{\circ} \mathrm{C}$

13. $Mass \ of \ calorimeter, stirrer, lid, cold\ water and\ solid =m_{3}=\ldots \ldots \mathbf{g}$

Calculations:
1. Mass of cold wate r $=m_{2}-m_{1}=\ldots . . g$
2. Mass of hot solid $=m_{3}-m_{2}=\ldots \ldots \mathrm{g}$
3. Rise of temperature of cold water and calorimeter $=\theta-t=\ldots . .^{\circ} \mathrm{C}$
4. Fall in temperature of solid $=T-\theta=\ldots .^{\circ} \mathrm{C}$

5. Heat gain by calorimeter, cold water and stirrer $=\left[\omega+\left(m_{2}-m_{1}\right)(\theta-t)\right]=\ldots \ldots$
6. Heat lost by solid $=\left(m_{3}-m_{2}\right) \times C \times(T-\theta)=\ldots \ldots$
7. Here, C is the specific heat of solid to be calculated.
According to principle of calorimeter, heat lost = heat gained

$\left(m_{3}-m_{2}\right) \times C \times(T-\theta)=\left[\omega+\left(m_{2}-m_{1}\right)(\theta-t)\right]$ $ \\ C=\frac{\left[\omega+\left(m_{2}-m_{1}\right)(\theta-t)\right]}{\left[\left(m_{3}-m_{2}\right)(T-\theta)\right]}=\ldots \ldots \operatorname{callg}^{\circ} \mathrm{C}$

Result:
Specific heat of given solid by method of mixture is $\ldots cal \mathrm{g}^{-1} \mathrm{c}^{-1}$

Precautions:
1. Sufficient solid power should be taken to cover the tip of thermometer properly.
2. Sufficient water should be taken in hypsometer.
3. Solid should be dropped quickly and gently.
4. Calorimeter should be polished from outside to avoid excessive radiation losses.
5. Temperature of cold water should not be below the dew point.