Explanation:
\(300\,K = (300 - 273)^\circ C = 27^\circ C\)
Given,\({R_{27}} = 0.3W\)
\({R_t} = 0.6\) (at temperature \(t^\circ C\)).
Temperature coefficient of resistance
\(\alpha = 1.5 \times {10^{ - 3}}^\circ {K^{ - 1}} = 1.5 \times {10^{ - 3}}^\circ {C^{ - 1}}\)
\({R_{27}} = {R_0}(1 + a \times 27)\)
\({\mathop{\rm or}\nolimits} {\mkern 1mu} \,\,0.3 = {R_0}(1 + 1.5 \times {10^{ - 3}} \times 27)\,\,\,\,\,\,\,\,(1)\)
\({\rm{Also}},{R_t} = {R_0}(1 + at)\)
\({\mathop{\rm or}\nolimits} {\mkern 1mu} \,\,0.6 = {R_0}(1 + 1.5 \times {10^{ - 3}} \times t)\,\,\,\,\,\,\,\,\,\,\,(2)\)
Dividing eq. (2) by (1), we get
\(\frac{{0.6}}{{0.3}} = \frac{{1 + 1.5 \times {{10}^{ - 3}}t}}{{1 + 1.5 \times {{10}^{ - 3}} \times 27}}\)
\({\phi _2}(1 + 1.5 \times {10^{ - 3}} \times 27) = 1 + 1.5 \times {10^{ - 3}}t\)
\({\phi _2} + 81 \times {10^{ - 3}} = 1 + 1.5 \times {10^{ - 3}}t\)
\({\phi _2} + 0.081 = 1 + 1.5 \times {10^{ - 3}}t\)
\(t = \frac{{1.081}}{{1.5\,\, \times \,{{10}^{ - 3}}}}\)
\( = 720.7\,^\circ C\)
\( = (720.7\, + 273)K = 993.7\,K\)