An alloy consists of n metals of mass m1,m2, m3, . . … . . , mn and

1.	An alloy consists of n metals of mass m1,m2, m3, . . … . . , mn and specific heat of the alloy, c?
Answer» Given, c is the specific heat of the alloy. Suppose that the alloy is heated through θºc. Now mass of the alloy, M = m₁ + m₂ + m₃+. . … . . +m_n. The amount of heat required to heat the alloy is given by Q = (m₁ + m₂+. . … . . +m_n)cθ. …(i) Also, Q = m₁c₁θ + m₂c₂θ + m₃c₃θ+. . … . . +m_nc_nθ …(ii) From the eqn. (i) and (ii) (m₁ + m₂ + m₃+. . … . . +m_n) cθ = (m₁c₁ + m₂c₂ + m₃c₃+. . … . . +m_nc_n)θ c = \(\frac{m_1c_1+m_2c_2+m_3c_3+.....+m_nc_n}{m_1+m_2+m_3+.....+m_n}\)

An alloy consists of n metals of mass m1,m2, m3, . . … . . , mn and specific heat of the alloy, c?

Answer»

Given, c is the specific heat of the alloy. Suppose that the alloy is heated through θºc.

Now mass of the alloy,

M = m₁ + m₂ + m₃+. . … . . +m_n.

The amount of heat required to heat the alloy is given by

Q = (m₁ + m₂+. . … . . +m_n)cθ. …(i)

Also, Q = m₁c₁θ + m₂c₂θ + m₃c₃θ+. . … . . +m_nc_nθ …(ii)

From the eqn. (i) and (ii)

(m₁ + m₂ + m₃+. . … . . +m_n) cθ

= (m₁c₁ + m₂c₂ + m₃c₃+. . … . . +m_nc_n)θ

c = \(\frac{m_1c_1+m_2c_2+m_3c_3+.....+m_nc_n}{m_1+m_2+m_3+.....+m_n}\)