Tag: calorimetry

Questions Related to calorimetry

$5$g of copper was heated from $20^{\circ}$ to $80^{\circ}$. How much energy was used to heat Cu? (Specific heat capacity of Cu is $0.092 cal/g ^{\circ}C$).

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $27.6$ cal

  2. $50$ cal

  3. $35$ cal

  4. $25.7$ cal

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Correct Option: A
Explanation:
Given,

Mass, $m=5\,g$

Specific heat capacity, $C=0.092\,cal/g \,^0C$

Change in temperature, $\Delta T=80\,^0C -20^0C=600^0C$

Heat required, $Q=?$

We have the equation,

$Q=m\times C\times \Delta T$

Then,

$Q=5\times 0.092\times 60=27.6\,cal$

2000 J of energy is needed to heat 1 kg of paraffin through $1^{\circ}C$. So How much energy is needed to heat 10 kg of paraffin through $2^{\circ}C$ ?

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. 4000 J

  2. 10,000 J

  3. 20,000 J

  4. 40,000 J

Show answer
Correct Option: D
Explanation:

$W= mc\theta$
$2000= (1000)c(1)$
$c= 2$ $J/g^oC$

we get value of c
Hence for $10 kg$ through $2^oC$,
$W= (10000)(2)(2)= 40000 J$

Which of the following properties must be known in order to calculate the amount of heat needed to melt 1.0kg of ice at $0^oC$? 
I. The specific heat of water 
II. The latent heat of fusion for water 
III. The density of water.

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. I only

  2. I and II only

  3. I, II, and III

  4. II only

  5. I and III only

Show answer
Correct Option: D
Explanation:

The latent heat is the heat required to change the state of unit mass of substance ,  therefore heat required to change the mass $m$ of substance  is given by ,

            $Q=mL$ ,  where $m=$ mass of substance , $L=$ latent heat
 here we have $m=1.0kg$ but we don't have value of $L$ (latent heat of fusion for water) so it is required .
    Density and specific heat of water are not required here , as it is clear from formula mentioned above .

One calorie is defined as the heat required to raise the temperature of $1$ gm of water by $1^o$C in a certain interval of temperature and at certain pressure. The temperature interval and pressure is?

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $13.5^o$ C to $14.5^o$ C & $76$ mm of Hg

  2. $6.5^o$ C to $7.5^o$ C & $76$ mm of Hg

  3. $14.5^o$ C to $15.5^o$ C & $760$ mm of Hg

  4. $98.5^o$ C to $99.5^o$ C & $760$ mm of Hg

Show answer
Correct Option: C
Explanation:

One calories is defined as the amount of heat required to raise the temp of $1\ gm$ of water from $14.5^oC$ to $15.5^oC$

in $760\ mm$ of $Hg$.

A copper ball of mass $100gm$ is at a temperature $T$. It is dropped in a copper calorimeter of mass $100gm$, filled with $170gm$ of water at room temperature. Subsequently the temperature of the system is found to b4 ${75}^{o}$. $T$ is given by then (Given: room temperature $={30}^{o}C$, specific heat of copper $=0.1cal/gm _{  }^{ o }{ C }\quad $)

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. ${ 825 }^{ o }C$

  2. ${ 800 }^{ o }C$

  3. ${ 885 }^{ o }C$

  4. ${ 1250 }^{ o }C$

Show answer
Correct Option: C
Explanation:
Final temperature of celomiter and its constant is given as
$To=75^o C$
$\Rightarrow \ 100\times 0.1\times (75-T)+100\times 0.1(75-30)+1.70 \times 1\times (75.32)$
$\therefore \ T=885^oC$

In a calorimeter of water equivalent $20g$,water of mass $1.1$kg  is taken at $288K$ temperature.If steam at temperature $373K$ is passed through it and temperature of water increases by $6.5^oC$ then the mass of steam condensed is:

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $17.5g$

  2. $11.7g$

  3. $15.7g$

  4. $18.2g$

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Correct Option: B

Steam at $100^oC$ is passed into $2.0$kg of water contained in a calorimeter of water equivalent $0.02$kg at $15^oC$ till the temperature of the calorimeter and its content rise to $90^oC$. The mass of steam condensed in kg is

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $0.301$

  2. $0.280$

  3. $0.60$

  4. $0.02$

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Correct Option: B

A copper calorimeter contains $100 g$ of water at $16^o C$. When $15 g$ of ice is added to it, the resultant temperature of the mixture is $4^o C$. Water equivalent of the calorimeter is

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $8 g$

  2. $12 g$

  3. $6 g$

  4. None

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Correct Option: D

The water equivalent of a 400 g copper calorimeter (specific heat =0.1 cal/$g^{ o }C$)-

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. $40g$

  2. $4000g$

  3. $200g$

  4. $4g$

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Correct Option: A

$50  g$ of ice at 0 C is mixed with $50  g$ of water at 20 C.The resultant temperature of the mixture would be

physics calorimetry heat exchange calorimeter measuring thermal quantities by the method of mixtures

  1. 10 C

  2. 0 C

  3. -10 C

  4. -35 C

Show answer
Correct Option: B
Explanation:

$50 g $ of Ice at $0^0C$ has a latent heat of

$ Q = m \times L = 50 \times 80 $ 

                    $ = 4000 cal $

Now for water to reach $0^{0}C$ without changing its state 

Heat released by water = $ mC _p  \Delta T$

                                      = $ 50 \times 1 \times 20  $

                                      = $1000 cal $

As the heat to be removed from water is less than the latent heat of $50g $ of ice, the resultant mixture stays at $0^0C $ temperature.