दो एक ही पदार्थ के ठोस गोलों के व्यासो का अनुपात 5 : 4 है तथा इनका ताप `227^(@)C` तथा `127^(@)C` है। यदि परिवेश का ताप `27^(@)C` हो तो दोनों गोलों के ठंडे होने कि दरों कि तुलना करो।

Explanation

किसी वस्तु कि शीतलन दर
`R = (sigmain_(r)A)/(J)(T^(4) - T_(0)^(4))`
`therefore (R_(1))/(R_(2)) = (A_(1)(T_(1)^(4) - T_(0)^(4)))/(A_(2)(T_(2)^(4) - T_(0)^(4))) = (4pir_(1)^(2)(T_(1)^(4) - T_(0)^(4)))/(4pir_(2)^(2)(T_(2)^(4) - T_(0)^(4)))`
`(R_(1))/(R_(2)) =((r_(1))/(r_(2)))^(2) [ (T_(1)^(4) - T_(0)^(4))/(T_(2)^(4) - T_(0)^(4))]`
दिया गया है -
`(r_(1))/(r_(2)) = (5)/(4)`
`R_(1) = 227^(@)C = 227 + 273 = 500 K`
`T_(2) = 127^(@)C = 127 + 273 = 400 K`
`T_(0) = 27^(@)C = 27 + 273 = 300 K`
`therefore (R_(1))/(R_(2)) = ((5)/(4))^(2)[(500^(4) - 300^(4))/(400^(4) - 300^(4))] = (25)/(16) xx (544)/(175) = (34)/(7)`
`therefore R_(1) : R_(2) = 34 : 7`