Latent Heat and conservation of energy

[rico22]

Homework Statement

A cooking vessel on a slow burner contains 11.0 kg of water and an unknown mass of ice in equilibrium at 0°C at time t = 0. The temperature of the mixture is measured at various times. During the first 50.0 min, the mixture remains at 0°C. From 50.0 min to 60.0 min, the temperature increases to 2.00°C. Ignoring the heat capacity of the vessel, determine the initial mass of ice.

Homework Equations

Q =mcΔT; Q= mL

c_water=4186
L_fusion=333000

Q_hot + Q_cold=0

The Attempt at a Solution

m_iceL_fusin+m_icec_waterΔT+m_waterc_waterΔT = 0

m_ice(333000) + m_ice(8372) + 92092 = 0

This gives me m_ice = 0.269kg but i know this is wrong. Any pointers would be greatly appreciated.

 

[CWatters]

During the melting phase all the energy goes into melting the ice (water stays at zero) so

M_ice * L_fusion = Power * Time_melt

After melting during the heating phase..

(M_water + M_ice) * C_water * ΔT = power * Time_heat

Two unknowns and two equations.

 

[rico22]

Thanks for the reply... I reworked the problem but I am still getting it wrong somehow...

 

[rico22]

ok now I got it... I mustve been doing something wrong with the calculations...how did you know to bring power into the formula?

 

[SteamKing]

What is the definition of power?

 

[CWatters]

...how did you know to bring power into the formula?

I started by writing out..

M_ice * L_fusion = E_melt

but then you get stuck because there isn't enough info in the problem statement to calculate the energy and the timing information hadn't been used.

Energy is related to power using...

Power = Energy/time

or

Energy = Power * Time.

I made the reasonable assumption that the heater element delivered constant power.

 

[rico22]

ok thank you!