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Question:

An unknown object of mass m_s, is added to water of mass m_w. The initial temperature of the unknown object is T_a and the initial temperature of the water is T_b. The system comes out to equilibrum with temperature T_f. Derive an experssion for the speicfic heat of the unknown object. Ignore the heat lost to the container, there are no phase changes during this process.

Answers:

EngFil

Mentor

Karma Points: 657

Date Posted: 6/29/2008 10:10:10 PM Status: Live

Asker's Rating: Lifesaver

Response:

HEat gained/lost by Object S = Heat gained/lost by Water        ( because you didn't specify which one gained/lost heat)
Heat = mcΔt

m_sc_s(T_{f -}T_a) = m_wc_w(T_{f -}T_b)          where c_sis the specific heat of the unknown object

c_s= m_wc_w(T_{f -}T_b)/m_s(T_{f -}T_a)

OR
Because we know heat capacity of water c_w to be 4.184 J/gC, we can substitute this so
c_s= 4.184m_w(T_{f -}T_b)/m_s(T_{f -}T_a)

That's the answer. Please dont forget to rate me. Feel free to ask additional questions.

miss.bossyy's Comment:

thank u

Kayen

Oracle

Karma Points: 21,845

(Ohio University Main Campus)

Date Posted: 6/29/2008 10:13:14 PM Status: Live

Asker's Rating: Helpful

Response:

Calorimetry problems are a bit tricky esp in using different units. But here there are no units involved; it is easy. If you have other qns send me a message.

Heat transferred is always either,
Q = m.c.ΔT due to change in temp ΔT; or

Q' = m.L due to phase change.

We assume the unknown object temp Ta > temp of water, Tb

Heat lost by the unknown object,

Q₁ = mc.ΔT = m_s.c_s.(T_a- T_f)

Heat gained buy water,

Q₂= mc.ΔT = m_w.c_w.(T_f- T_b)

Since there is no other loss or gain, these4s two must be equal

(Principle of calorimetry).

m_s.c_s.(T_a- T_f) = m_w.c_w.(T_f- T_b)

Sp heat capacity of the unknown object,

c_s = m_w.c_w.(T_f- T_b)/[m_s(T_a- T_f)]

Here cw is sp heat of water = 1 cal/g^oC or 4.186 J/g^oC.

miss.bossyy's Comment:

I wish I could give u more points...but I really appericate your help:-)...thanks u so much...u r genius

Kayen (Enjoys helping you uderstand..)

Please do not forget to Rate my Response.

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Please help (Thermodynamics)

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