"46.7 g of water at 80.6 oC is added to a calorimeter that contains 45.33 g of water at 40.6 oC. If the final temperature of the system is 59.4 oC, what is the calorimeter constant (C calorimeter)

When hot water is added to the calorimeter, the amount of heat released by the hot water will be equal to the amount of heat absorbed by cold water and calorimeter.

[tex]Heat_{\text{absorbed}}=Heat_{\text{released}}[/tex]

The equation used to calculate heat released or absorbed follows:

[tex]Q=m\times c\times \Delta T=m\times c\times (T_{final}-T_{initial})[/tex]

[tex]m_1\times c_1\times (T_{final}-T_1)=-[(m_2\times c_2)+c_3](T_{final}-T_2)[/tex] ......(1)

where,

q = heat absorbed or released

[tex]m_1[/tex] = mass of hot water = 46.7 g

[tex]m_2[/tex] = mass of cold water = 45.33 g

[tex]T_{final}[/tex] = final temperature = 59.4°C

[tex]T_1[/tex] = initial temperature of hot water = 80.6°C

[tex]T_2[/tex] = initial temperature of cold water = 40.6°C

[tex]c_1[/tex] = specific heat of hot water = 4.184 J/g°C

[tex]c_2[/tex] = specific heat of cold water = 4.184 J/g°C

[tex]c_3[/tex] = specific heat of calorimeter = ? J/g°C

Putting values in equation 1, we get:

[tex]46.7\times 4.184\times (59.4-80.6)=-[(45.33\times 4.184)+c_3](59.4-40.6)[/tex]

[tex]c_3=30.68J/g^oC[/tex]

Hence, the specific heat of calorimeter is 30.68 J/g°C