Solve ell(345/54)=-A/8.314(1/25+273-1/273)

$$\ell ( \frac { 345 } { 54 } ) = \frac { - A } { 8.314 } ( \frac { 1 } { 25 + 273 } - \frac { 1 } { 273 } )$$

Evaluate

$$\frac{6250A}{169094289}$$

Solution Steps

Add 25 and 273 to get 298.

$$\frac{-A}{8.314}\left(\frac{1}{298}-\frac{1}{273}\right)$$

Least common multiple of 298 and 273 is 81354. Convert \frac{1}{298} and \frac{1}{273} to fractions with denominator 81354.

$$\frac{-A}{8.314}\left(\frac{273}{81354}-\frac{298}{81354}\right)$$

Since \frac{273}{81354} and \frac{298}{81354} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-A}{8.314}\times \frac{273-298}{81354}$$

Subtract 298 from 273 to get -25.

$$\frac{-A}{8.314}\left(-\frac{25}{81354}\right)$$

Divide -A by 8.314 to get -\frac{500}{4157}A.

$$-\frac{500}{4157}A\left(-\frac{25}{81354}\right)$$

Multiply -\frac{500}{4157} times -\frac{25}{81354} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-500\left(-25\right)}{4157\times 81354}A$$

Do the multiplications in the fraction \frac{-500\left(-25\right)}{4157\times 81354}.

$$\frac{12500}{338188578}A$$

Reduce the fraction \frac{12500}{338188578} to lowest terms by extracting and canceling out 2.

$$\frac{6250}{169094289}A$$

Expand

$$\frac{6250A}{169094289}$$

Solution Steps

Add 25 and 273 to get 298.

$$\frac{-A}{8.314}\left(\frac{1}{298}-\frac{1}{273}\right)$$

Least common multiple of 298 and 273 is 81354. Convert \frac{1}{298} and \frac{1}{273} to fractions with denominator 81354.

$$\frac{-A}{8.314}\left(\frac{273}{81354}-\frac{298}{81354}\right)$$

Since \frac{273}{81354} and \frac{298}{81354} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-A}{8.314}\times \frac{273-298}{81354}$$

Subtract 298 from 273 to get -25.

$$\frac{-A}{8.314}\left(-\frac{25}{81354}\right)$$

Divide -A by 8.314 to get -\frac{500}{4157}A.

$$-\frac{500}{4157}A\left(-\frac{25}{81354}\right)$$

Multiply -\frac{500}{4157} times -\frac{25}{81354} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-500\left(-25\right)}{4157\times 81354}A$$

Do the multiplications in the fraction \frac{-500\left(-25\right)}{4157\times 81354}.

$$\frac{12500}{338188578}A$$

Reduce the fraction \frac{12500}{338188578} to lowest terms by extracting and canceling out 2.

$$\frac{6250}{169094289}A$$