The heat lost to the environment by the calorimeter is given by q(T-Tatm)t, wher

Question

The heat lost to the environment by the calorimeter is given by q(T-Tatm)t, where T is the temperature of the calorimeter, Tatm is the temperature of the surrounding air and t is the length of time over which the heat loss occurs. If the temperature is changing with time then this expression becomes: The heat lost to the environment by the calorimeter is given by q(T-Tatm)t, where T is the temperature of the calorimeter, Tatm is the temperature of the surrounding air and t is the length of time over which the heat loss occurs. If the temperature is changing with time then this expression becomes:

Explanation / Answer

the gragh T with respected to t is a straight line. so we have. (Ta-T)/(ta-t)=(Ta-Tb)/(ta-tb). so T-Ta=(t-ta)*(Ta-Tb)/(ta-tb). so T=(t-ta)(Ta-Tb)/(ta-tb)+Ta integral of (T-Tatm)*dt = T*dt-Tatm*dt so t*(Ta-Tb)/(ta-tb)*dt -(ta*(Ta-Tb)/(ta-tb)+Tatm)*dt. integral of it. t^2(Ta-Tb)/(ta-tb)/2 - (ta*(Ta-Tb)/(ta-tb)+Tatm)*t so its value (Ta^2-TA^2)(Ta-Tb)/(ta-tb)/2 - (ta*(Ta-Tb)/(ta-tb)+Tatm)*(Ta-TA)

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