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The problem statement, all variables and given/known data

Question 1.

A student uses some equipment that can add energy at a constant rate to some water contained in a copper calorimeter can. To keep the temperature of the water uniform, the student stirs the water with a copper stirrer. Together, the calorimeter can and the stirrer have a mass of m_{c}and a specific heat of c_{c}and the water has a mass of m_{w}and specific heat of c_{w}.

The initial temperature of the water is T_{0}, and the student begins adding energy to the system at a constant rate of P watts.

Assuming there is no energy loss from the system, derive an expression for the temperature, T, of the system as a function of time, t.

(Hint: the rate at which the energy is added, P = [tex]\frac{dQ}{dt}[/tex] where dQ = (m_{c}c_{c}+m_{w}c_{w})dT.

Substitute,rearrange and integrate).

Question 2.

Consider a copper calorimeter can with a copper stirrer has a total mass m_{c}and specific heat c_{c}.

- It contains a msss m
_{w}of water of specific heat c_{w}at a temperature of T_{i}^{o}C.- A mass m
_{i}of ice at 0^{o}C is added to the calorimeter.- The heat of fusion of ice is L
_{i}.- All the ice melts and the temperature of the can, stirrer, and contents falls to T
_{f}^{o}C (which is above 0^{o}C)

(a) Presuming that there is no heat energy gained or lost by the system, write down an equation representing conservation of energy for the system. Indicate clearly what each terms in this equation represents.

(b) Hence, find an expression for the latent heat of fusion of ice, L_{i}, in terms of the other variables in your equation. (Show all steps)

The attempt at a solution

Question 1

P = [tex]\frac{dQ}{dt}[/tex] = [tex]\frac{(m_cc_c+m_wc_w)dT}{dt}[/tex]

dT = [tex]\frac{P dt}{m_cc_c+m_wc_w}[/tex]

T = [tex]\frac{P}{m_cc_c+m_wc_w}[/tex][tex]\int_{t_i}^{tf} dt[/tex]

T = [tex]\frac{P}{m_cc_c+m_wc_w}[/tex][tex] \left[ t \right]_{t_i}^{t_f}[/tex]

T = [tex]\frac{P(t_f-t_i)}{m_cc_c+m_wc_w}[/tex]

Question 2 a

Q_{i}= -Q_{w+c}

Q_{i}- Q_{w+c}= 0

m_{i}L_{i}+ m_{w+c}c_{w+c}[tex]\Delta[/tex]T = 0

m_{i}L_{i}+ (m_{c}c_{c}+m_{w}c_{w})(T_{f}- T_{i}) = 0

Question 2 b

m_{i}L_{i}+ T_{f}(m_{c}c_{c}+m_{w}c_{w}) - T_{i}(m_{c}c_{c}+m_{w}c_{w}) = 0

m_{i}L_{i}= T_{i}(m_{c}c_{c}+m_{w}c_{w}) - T_{f}(m_{c}c_{c}+m_{w}c_{w})

.: L_{i}= [tex]\frac{(T_i-T_f)(m_cc_c+m_wc_w)}{m_i}[/tex]

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# Specific and Latent Heat - Pre-laboratory work

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