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see in attachment.
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To solve this problem we use the principle of
Heat lost by one substance = Heat gained by the other
One substance loses heat and cools down to temp t from t¹
Other substance gains heat and heats up to temp t from t²
Therefore, t¹>t>t²
Heat lost by one = m¹s¹∆T¹ = m¹s¹(t¹-t)
Heat gained by other = m²s²∆T² = m²s²(t-t²)
m¹s¹(t¹-t) = m²s²(t-t²)
m¹s¹t¹-m¹s¹t = m²s²t-m²s²t²
m¹s¹t¹+m²s²t = t(m¹s¹+m²s²)
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