Question

Water’s specific heat capacity is 4.186 joules/gram degree Celsius. Mercury’s specific heat capacity is 0.140 joules/gram degree Celsius.


Water and mercury are put into three identical bowls:


Bowl A contains 20 grams of water.

Bowl B contains 40 grams of water.

Bowl C contains 20 grams of mercury.

The bowls start at the same temperature, and then the same amount of heat is added to each bowl. Order the bowls from coolest to warmest, based on their final temperatures.


bowl A

Answer 1

Answer:

The order of bowls from coolest to warmest based on their final temperatures will be:

Bowl B < Bowl A < Bowl C

Explanation:

Same amount of heat is added to each bowl = Q

Bowl -A:

Mass of the  water ,m= 20 g

Initial temperature of the water = $T_1$

Final temperature of the water =$T_2$

Heat capacity of the water= c = 4.186 J/g°C

Change in temperature of the water = $\Delta T_1=(T_2-T_1)$

$Q=mc\times \Delta T_1=mc\times (T_2-T_1)$

$Q=20 g\times 4.186 J/g^oC\times \Delta T_1$

$\Delta T_1=\frac{Q}{m\times c}$

$\Delta T_1=\frac{Q}{20 g\times 4.186 J/g^oC}$..[1]

Bowl -B:

Mass of the  water ,m' = 40 g

Initial temperature of the water = $T_1$

Final temperature of the water =$T_3$

Heat capacity of the water= c = 4.186 J/g°C

Change in temperature of the water = $\Delta T_2=(T_3-T_1)$

$Q=m'c\Delta T_2=mc\times (T_3-T_1)$

$Q=40 g\times 4.186 J/g^oC\times \Delta T_2$

$\Delta T_2=\frac{Q}{m'\times c}$

$\Delta T_2=\frac{Q}{40 g\times 4.186 J/g^oC}$..[2]

Bowl -C:

Mass of the mercury ,m''= 20 g

Initial temperature of the mercury = $T_1$

Final temperature of the mercury =$T_4$

Heat capacity of the mercury= c' = 0.140 J/g°C

Change in temperature of the water = $\Delta T_3=(T_4-T_1)$

$Q=m''c'\Delta T_3=mc\times (T_4-T_1)$

$Q=20 g\times 4.186 J/g^oC \times \Delta T_3$

$\Delta T_3=\frac{Q}{m''\times c'}$

$\Delta T_3=\frac{Q}{20 g\times 0.140J/g^oC}$..[3]

Taking ratio of [1] , [2],and [3]

$\Delta T_1 :\Delta T_2 :\Delta T_3$

=$\frac{Q}{20 g\times 4.186 J/g^oC}:\frac{Q}{40 g\times 4.186 J/g^oC}:\frac{Q}{20 g\times 0.140J/g^oC}$

$\Delta T_1 :\Delta T_2 :\Delta T_3$ = 1 : 0.5 : 29.9

As substance with larger value in change in temperature will have higher temperature on addition of energy. So, the order of bowls from coolest to warmest based on their final temperatures will be:

Bowl B < Bowl A < Bowl C

Answer 2

Answer: Bowl B < Bowl A  <  Bowl C

Explanation: